Solving Equations with Logarithms Pt 1

PLEASE NOTE my final answer at 10:26 should be 3.968. There is an annotation correction but you can only see this if using FLASH.
In a three part video I do many examples of solving equations using logarithms to move the variable out of the exponent. In part two we remove logarithms from the equation to solve for X.
Here are my other PreCalculus lessons involving Logarithms
www.profrobbob.com/pre-calculu...
Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage / profrobbob

[@zainawarriorpriness]

I'm a student in the scientific major in Jordan, and sometimes I face problems in understanding some topics. A friend of mine told me to watch your videos and I'll be able to understand everything in less than 20 minutes.I couldn't believe it until I saw them myself. Your marvelous way in teaching makes Math easy,fun and enjoyable. You are truly gifted! God bless you, and keep up your GREAT work! students rely on you all over the world in understanding Math.

[@hudsondean5151]

Best online teacher out there.

[@profrobbob]

+Hudson Dean thanks for the testimonial and for subbing!

[@profrobbob]

Thank you for watching and the kind words:) I hope you do great in your class!

[@profrobbob]

YES...that would have been a little simpler! Thanks for watching and helping out:)

[@MRSsamadi]

i have tears in my eyes after 2 years, i now understand log

[@profrobbob]

You're welcome! And THANKS for watching part 1 & 2:)

[@profrobbob]

I'm glad to hear they are helping so much...thanks for watching and please be sure to share my channel with your fellow classmates!

[@profrobbob]

Thank you for liking and subscribing! Please continue to support my channel growth by sharing it with your friends and classmates:D

[@profrobbob]

You can count on that!...Thanks for liking and commenting and please help me grow by sharing with others:D

[@profrobbob]

I'm glad you are finding my videos helpful for your exam preparation and I hope they give you that extra confidence you need to ace that exam! Be sure to share with your other classmates too:D

[@profrobbob]

Go to my channel home page and you will find plenty more:) Thanks for watching!

[@profrobbob]

Thanks...I have chosen to do my videos as full lessons rather than just problem solving. That's the way I was taught and felt like there were plenty of short video options already available. I'm sorry if they are more than your are looking for but thanks for taking the time to watch...maybe someday you will need that additional help and know where to find me:)

[@profrobbob]

:):):):) Thank you so much for the great comment. I am very excited you like my videos so much:D I hope you do great next year. I am sure you will, rarely does someone as motivated as you struggle in math. Please help me by spreading the word about my math channel and remember the ads support my efforts as well as KZbin...though they are annoying. I hope to hear about your AWESOME grades in the upcoming school year!

[@profrobbob]

You are very welcome....keep watching and sharing with your friends if you find these videos helpful:) My channel grows through the support of subscribers like you...Thanks!

[@profrobbob]

I LOVE to hear when that light comes on and shines so bright!!!! Thanks for watching:)

[@profrobbob]

Thank you very much for the kind words and the suggestion. I appreciate the support very much:D

[@profrobbob]

You're welcome...thanks for the comment and support by subscribing!...and glad you found my examples helpful.

[@profrobbob]

And THANK YOU for taking the time to send a comment...I'm happy to hear that my videos are helping you more that the ones supplied to you:) Congrats on being back in school too. Thanks for seeking extra help and stopping on my channel...and supporting by subscribing!...so please share my channel and help me groW!

[@profrobbob]

Haha...I do a little calligraphy here and there. Thanks for watching and the nice comment. I hope I can continue to help with your math and handwriting:)

[@profrobbob]

I think it is pure awesomeness that you like my video and I could help all the way from the US!!! Thanks for watching and the nice comment:D

[@profrobbob]

Thanks for watching and liking and I hope this means you will return to my channel for extra help when you need it!

[@profrobbob]

And THANK YOU for that heartfelt compliment:) I'm glad you sought out extra help and found my channel...I hope since you subscribed that this will be the start of an enjoyable learning experience from Tarrou's Chalk Talk!

[@profrobbob]

Glad you found my video so helpful! I hope you will continue to choose my channel to get extra help from, and please be sure to share with your friends:D

[@profrobbob]

Thank you for letting me know the link was dead. I remove videos sometime and repost them when corrections are made because annotation don't show up on iPads. The weird thing though, is the second part does not have a later posting date...so I don't know why the link did not work? Anywhoo, thanks for the heads up and the very nice words:)

[@profrobbob]

@osvideosdojoao Sorry about that. Since I am new at this I also just discovered my anotations that I add to correct my mistakes can't be seen on ipads, iphones, and I guess anything portable that is not a laptop. So I will have to find another way to correct my minor errors. I hope the video was still helpfull:)

[@eliezerelefant1134]

Words cannot explain the gratitude I have to you for taking the time and making these videos. I would be totally lost in my pre-calculus course with out you. May God bless you with may years of health and happiness!

[@profrobbob]

Eliezer e thank you for choosing my channel to learn from and taking the time to "thank the teacher" ! Please like, subscribe, support the ads, share and spread the word to help these free educational channel grow and remain free:D

[@profrobbob]

Thank you for that motivating comment! Students like yourself are one of the reasons why I love to do what I do. And as long as I can continue to "make a difference" I will continue to make these videos...my dream is to groW my channel and continue to offer FREE math help for everyone, everywhere by "Making Math FUN while learning" You can start helping by sharing my channel with your friends:D Thanks for supporting.

[@bofesusbofesus]

Sir, I want to thank you for having the enthusiasm and loud voice that is needed for a student struggling in math to finally learn the material that is needed. PLEASE KEEP MAKING THESE. YOU'RE AWESOME!!!!

[@kakashi1414]

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[@heathermoser6220]

I just want to say thank you so much! I have a Algebra II test tomorrow and I understand it so much more now! I love how you give so many examples they help the most!!! Thanks and God has blessed you with great math teacher talents!!!

[@jaymanji3293]

I definitely will be sharing these videos with other classmates and people who need help with calculus, precalculus, and other math classes in the future! Though I was really nervous going into my exam, reviewing with this channel has definitely eased some of those nerves!

[@profrobbob]

Thanks for saying so...and THANK YOU for liking and subscribing to my channel and supporting my efforts to help me groW! (or come up with some outrageous BAM! video that would get a million hits in a day...lol)

[@profrobbob]

Thanks. And thank you for supporting and subscribing...please spread the word throughout the "Kingdom":D

[@profrobbob]

The Power Rule of Logs allows you to drop down the exponent with the variable and it becomes (3r-1)Log5=(2r+5)Log6. You can use Ln too. Find the decimal answer of Log5 and Log6 and then distribute that number through each respective parenthesis and finish solving for r.

[@Siennex]

Glad that I found your channel and subbed. Your explanation is way way better than my textbook and BAM!! I managed to ace my class test! Thank you so much!! =)

[@raphaebaetiong5504]

I was having trouble with my Trigonometry class. I found your videos and they helped out big time! Your hand writing is awesome as well. Definitely earned a sub.

[@profrobbob]

+Raphae Baetiong thanks for watching and glad to hear they are helping! Please tell all your friends to watch, sub and share too:D If you need a break from math I have some cursive lessons too:)

[@profrobbob]

I feel an A in your future!...I hope you continue to find my channel helpful, Thanks for watching and supporting.

[@profrobbob]

The rational exponent 5 ^(1/2)? Rational exponents are power/root. The 5 had a power of 1 and the square root has a root of 2. Thanks for watching:)

[@jessybradine4102]

I'm angolan and study in Brazil. I would like to say that with your teach way I can totally understand EVERYTHING, I don't understand in the classroom .Although the video be in English helps to learn more and more. Thank you, God bless you sir! You're an amazing teacher!

[@profrobbob]

You're welcome Jéssica Nadine and THANK YOU for watching, learning, subbing to my channel and taking the time to share your experience! It's nice to hear that my videos are helping you understand your math lessons and maybe even a little english at the same time...that really put's a smile on my face:)

[@jessybradine4102]

:D

[@profrobbob]

:)

[@profrobbob]

Thank you for watching!

[@profrobbob]

THANK YOU for watching:)

[@leedahoney]

I really do wish that my Pre-Calculus taught like you. The way she teaches is really hard to understand and whenever we ask her how to solve a problem, she would question us back with very confusing questions. Thank you so much for posting up these videos too! I understand these logarithm equations way better now!! :)

[@profrobbob]

I'm glad you took the time to seek out help and choose my channel to watch and learn from! Sounds like you should tell the rest of your class where to find my videos:)…and don't forget to support and SUBSCRIBE!

[@vienlouis6637]

Sameee. we dont get teachers like you at school.

[@elizabethdean6662]

Holy cow! 10 years later I visited a tutor and scoured websites and books for the information you provided in less than 10 minutes! THANK YOU!

[@profrobbob]

You are very welcome...thanks for seeking outside help and choosing this channel to watch...BAM!!! Don't forget to like, subscribe and share this free resource with EVERYONE now that you found us:)

[@labellina12]

Seriously my favorite precalc tutor! I go straight to your videos for help!

[@profrobbob]

Chandler Reyes thanks for choosing my channel to sub to and learn from!

[@IIIDVIII]

Some viewers may appreciate you changing the link to the second video to link to your second take, instead of the removed video. I also want to take this time to say, THANK YOU! You're a great video teacher. Keep up the great work!

[@profrobbob]

For your first question you need move the exponent of 3 down as a coefficient, divide both sides by 3, and then take the equation out of log form. The second equation you need to start by taking the log or ln of both sides so you can move the exponents down with the variables so you can solve for r. I hope these tips along with my three videos can help.

[@profrobbob]

Thanks for watching!

[@profrobbob]

Rewrite ln2+lnx as ln(2x)=5...then you can put the equation into exponential form (or make both sides an exponent of e) and you get 2x=e^5. Divide both sides by 2 and you have your answer:) Thank you very much for watching!

[@profrobbob]

Thanks for the "thumbs up" approval ranking!!!...and thank you for showing your support and subscribing. Now BAM!...go spread the word about my channel to all your friends:D

[@yinellyrodriguez830]

Sometimes I don't know where he's going to Jump from (in the beginning of the video, either left or right? Lol. LOVE IT!!!!

[@profrobbob]

Yinelly Rodriguez LOL...I love it too that I can keep you interested and returning for more:) Thanks for watching and subbing!

[@reverence.607]

you are a great professor that knows how to put all types of examples that are actually useful unlike other youtube channels that put examples that are common sense and do not help you on your homework since they are easy examples

[@profrobbob]

You are really welcome...and thank you for "liking" my videos and the fantastic compliment! Feel free to send your tuition to my donation button instead...I'm sure I could calligraphy a nice diploma for you when you're done...hahahaha:)) I really do appreciate your support by choosing my channel to learn from!

[@profrobbob]

start with combining the left side to ln((2x/5)=3, put into exponential form e^3=(2x)/5, multiply by 5 and divide by 2

[@profrobbob]

BAM!!!…thanks again for watching Diana:)

[@profrobbob]

THANK YOU SOooo much for taking the time to send me such an amazing review! Let me start with my saying how mush I love the words..."You make math Fun"...also loved hearing that you shocked your teacher...as a teacher I can tell you we love it when a student comes to class prepared, it makes our job so much easier. I'm blessed with alot of great students in my class as well as loyal on-line students like yourself...but you can never be reassured enough that what you're doing is appreciated:)

[@shilorich4646]

This man's penmanship has FLAWLESS fluidity. I love looking at it!

[@profrobbob]

THANKS! If you need a break from math I even have a few cursive videos available...BAM!!!

[@profrobbob]

You're welcome!!! Keep watching:)

[@bleedy13]

wonderful video. I enjoy your lively attitude while you teach, it keeps me engaged.

[@profrobbob]

thanks for watching...please sub and share as often as possible!

[@deeqaisse6936]

THANK YOU SOOOOOO MUCH!!! you are a lifesaver! I passed my final exam because of your videos :)

[@profrobbob]

deeqa isse you are SOOOOOOOO welcome!!! CONGRATULATIONS and thanks for studying with #ProfRobBob

[@gilbertopena2881]

Wow, someone give this guy a medal!

[@profrobbob]

Send it on…I don't have a medal yet after 18 years of teaching:(…lol THANK YOU Gilberto for watching, liking, and subscribing…please share my channel with others and remind them to do the same to show their support of these FREE education channels:)

[@shanksroger8348]

I'm having a hard time in my algebra and trigonometry. Thanks to you sir I can understand better and learn more than my professors! Cheers :D

[@profrobbob]

Thanks for taking the time to search for the additional help you needed and chose #ProfRobBob to watch, learn and subscribe to! With study skills and that kind of motivation I'm sure you will pass both classes like BAM!!! Shanks Roger ! Please share your experience and my channel with your friends and classmates and remind them to like, subscribe, support the ads, spread the word thru social media, and tell all their friends to do the same....Our dream: 100,000 subscribers by 2015!

[@georgesadler7830]

Professor RobBob, thank you for a very exciting video/lecture on Solving Equations with Logarithms Part One. These problems continue to be simple to follow on a step-by-step basis. Students should also know the laws of Logarithms and how to use them for solving problems.

[@mikevega6655]

After watching 2 of your videos I was able to figure out every question I missed on my midterm in a matter of minutes. I plan on watching our videos again for my final tomorrow as they make the subject matter, less foreign. I enjoy your energetic style of teaching and only wish more teachers shared your passion. Great Job man and thanks for putting up these insightful videos.

[@profrobbob]

John Doe THANKS:) And thanks for choosing my channel to study with...I hope you passed that final like BAM!!! If so, please be sure to like, subscribe and share my channel with all your friends and classmates as well as the teacher:D

[@briankeith5350]

GREAT VIDEO MR BAM!!! I am doing an online (Distance Education) course for College Algebra and Trig as a refresher before I move on to my STEM classes such as Calc I-III, Chem as well as Physics next semester. This online experience has been horrible as for as support from the professor and the teaching method- well the teacher is me--- has ended up being very difficult. I realize how much I miss the interaction in a classroom environment and the need to be able to ask questions in class when I do not understand something. That is where you have come in. I know watch your videos before I begin each new chapter and then embark upon the assignments and if there is any doubt, I just rewatch your video until you answer or solve that particular question/doubt (which you do about 95% of the time). I can not THANK YOU ENOUGH, YOU HAVE BEEN THE LIGHT AT THE END OF THE TUNNEL. REALLY WITHOUT YOUR VIDEOS I WOULD BE IN A BAD SITUATION. There are other videos out there, but no one has yet to be quite as detailed or concise as your videos, at least in my opinion. I was actually using a pay tutor website for videos until I found you about a month ago. I do not need to do this anymore. I will be making a donation Prof T soon and YOU ARE TO BE GRACIOUSLY COMMENDED ON YOUR DEDICATION AND FREE HELP YOU GIVE US MATH STUDENTS. YOUR GENEROSITY IS BEYOND BELIEF. Ok, back to doing my homework as you so often tell us to do. Practice, practice, practice..... BAM!! I AM OUTTA HERE!!!

[@profrobbob]

brian keith haven't been referred to as Mr Bam until now:) Love it! Sorry to hear you are having such a bad online experience but I'm extremely happy to hear that my channel is helping fill the void of the in-class interaction. We do hear that complaint quite often though:( Hopefully, as the amount of online classes continue to grow the teaching tools will advance as well. In the meantime it sounds like you have the drive, determination and study skills to make the most of a less than ideal situation...which is what will get you that diploma in the end! Looks like I won't be able to help you much past Calc 1 but as long as I can, I hope you will continue to enjoy my channel and find the help you need. Did you check out my website?...you might find it easier to search from. www.profrobbob.com (there is even a printable flyer you could post at school for us:) Thanks for taking the time to send such an appreciative and inspiring comment and for sharing your learning (or lack of) experience with us...students like you are the reason why we work so hard to groW this channel and keep these lessons FREE for everyone who is willing to invest the time it takes to learn. Full-time teaching and KZbin is like having 2 full-time jobs...but as long as my wife and I feel like the reward is greater than the work we will keep doing all we can to continue it's growth. Which is another reason we continually ask students to like, subscribe, support the ads, share thru social media's, with classmates, friends and teachers and to keep supporting and sharing...that's what you can do to help us since you are 100% on point of how to get the most out of this channel:) Please keep us posted on your progress...you already feel like one of my own students...BAM!!! Best Regards, Rob & Cheryl

[@ulyssab]

Thanks

[@profrobbob]

uly b you're welcome:)

[@briankeith5350]

Mr Bam it must be time consuming.... heck I am having trouble with just 2 online classes now... so I am can relate to your busy busy schedule... yes I know about your website and have gone there as well and I do like the videos now after I watch them. I will be seeing you here, just keep the videos coming..... see ya, now go do your homework!!

[@kimberlydiaz3600]

You just saved my life. I have a test on this tomorrow and now i finally understand. Thank you for being such a great help.

[@profrobbob]

Happy to help you stay afloat! Thanks for subscribing and I hope you passed that test like BAM!!!

[@profrobbob]

Could I ask what math class you are in. I don't remember ever seeing problems like yours in the trig books I have taught from, or PreCalculus with sin and cos in the exponents in an equation like yours. While I am working on Calculus videos, I am also refreshing my own skills as I go. I am not familiar working with problems like yours sorry.

[@profrobbob]

If you need your answer in exact form... You will mult both sides by log(2) and then move up the 2x to be an exponent. Make both sides of the equation an exponent of 10 so you can cancel out the log functions. This will give you the equation 0=2^(2x) + 2^x -12. The coefficients of the first and second term is 1, remember 2 is the base of the exponent, so this equation is factorable. One factor once set to 0 has no solution, while the other factor once set = 0 gives the soln x=log(3)/log(2).

[@losthighwaygnr3685]

Incredibly helpful as always Prof ! Thank you so much for all these lessons ( I will continue to spread the word ;)

[@profrobbob]

+LostHighwayGNR THANKS...we only need a little more than 4,500 subscribers to get that silver play button award...BAM!!!

[@johnelliot11]

I had so many plans for the summer...and now i cant do anything but math...i am so addicted to your videos sir! you honestly make me love mathematics and do it for fun! grade 12 next year.... so i wanted to get a head start and i got the precalc and calc textbook....but after watching your talks i don't feel like studying from the textbook....you're doing great for this world! giving everyone the precious gift of knowledge....may God bless you!! :D

[@mr.danielolivobapctcna8322]

You are great! I'm a college student with an Associates degree and your videos are extremely helpful with my class notes. Keep up the good work! Thank you.

[@laloweed]

"BAM!" is my favorite part of your videos lol

[@superfluffyqt]

Ugh, why didn't I find these videos earlier in the semester? Maybe I'd have an A. Thank you SO much for taking the time for making these very helpful videos! Come teach my class, please :-) Hopefully I'll do good on my math test tomorrow, I've been watching your videos and doing my study guide with it which is helping tremendously. Thank you again!! YOU'RE AWESOME

[@profrobbob]

BAM!!!…you found me now and I hope this means you will tell all your friends and classmates where to find me and remind them to support and SUBSCRIBE! You're very welcome and I'll be waiting to hear about that "A" you get today…

[@peterandriszak8777]

Your videos are very helpful I have a quiz Wednesday,so thanks for the help!

[@nityabhattarai7824]

Dude, you're the best. I literally only watch your videos.

[@profrobbob]

Thanks for watching and supporting...I hope your sharing this channel too:D

[@Spartan_girl134]

your videos help me remember things i learned 3 or more years ago. Thank you for the videos

[@profrobbob]

+Alycea Heredia you're welcome...thanks for watching and subbing and please keep sharing:D

[@ccl8631]

KZbin can sometimes be a wormhole where you lose hours of your life to cat video after cat video. Your math lessons are a healthy antidote to that. Thanks!

[@profrobbob]

More videos?!...thanks for all the kind words and positive reinforcement. Don't forget that liking, subscribing and spreading the word thru social media helps educational channels like mine groW!

[@danielmohamoud8887]

ProfRobBob pls how to do this 2*3^2x=12? two multi 3 With Power of 2x Equal 12 this seems hard

[@danielmohamoud8887]

daniel mohamoud oh ... it was hard but i focus on ur video then i solve it easily thank so much

[@profrobbob]

daniel mohamoud practice makes perfect...thanks for not giving up until you "solved it"!

[@profrobbob]

I don't remember how I incorrectly got 2.635, but if you wrap the numerator in parenthesis or calculate the numerator completely then divide by 3 you get 3.968

[@profrobbob]

I did work through the mechanics like you suggest in my video introducing Logarithms...but I am sure most people to not watch my videos as a complete series.

[@profrobbob]

Thank you...and "when" you pass that final, let me know!!!

[@sarahalexis74]

Thank you! I am 38 years old and taking college algebra. Your videos are a LIFESAVER and so much better than the ones supplied by Pearson's My Math Lab platform. THANK YOU for making these vids!

[@profrobbob]

Where did 2.64 come from? The log(41) equals 1.61

[@profrobbob]

Do you have an answer to check your work with?

[@robandsar1]

Thanks for explaining how to set this up in a calculator!!!! i was setting up the problem right just entering in the calculator wrong.....it was driving me crazy but now i know thanks to you! i appreciate the work you have done with these videos and thank you!!!

[@profrobbob]

You're welcome, thanks for liking and learning from this channel! Please sub and share it with everyone to help us keep growing and remain free for everyone:D

[@profrobbob]

I just typed your first question into a calculator and got -2.9029. As far as your second problem start by taking the log of both sides of the equation, any base of log is fine. That will allow you to drop down the exponents with the variables. Distribute log2 through x+1 and log5 through 1-2x...continue solving the linear equation that is left.

[@TheBrendon575]

one of the best ive seen on youtube ! :D /// really easy to follow & well explained.

[@DumPlingZoup]

thank you for your beautiful teaching. i wish there were more teachers like you. i feel much more confident now with logs just by watching a few of your lessons. i subscribed and you're my new teacher now. lol. thanks again.

[@fsamaroo337]

THANK YOU!!! I have been trying to figure out how to solve the last problem you worked out that I've been stuck for quit a while... Only hope I can remember how to solve it when I take my test! BTW great job! and thanks for taking the time to make these videos that help us non-math geniuses.

[@profrobbob]

WOW...you have really been busy watching and learning haven't you?! Thanks again and don't forget to share with your friends:D

[@graingerous16]

you've accomplished in 2 minutes what my trig teacher has failed to accomplish in four months

[@profrobbob]

Glad you enjoyed my attempt at humor...it helps keep my students awake during the day! Please share my channel if you found it helpful...your friends could be my future subscribers:))

[@mekkajones8711]

oh, also when I posted I meant to put "ln(e3)" as "ln(2x)-ln(5)=ln(e^3)" so does that mean that the ln(e^3) cancel since in the videos you say the ln and e cancel each other out?

[@dogeeatsveggies]

you know what sir... YOU SAVED A PART OF MY LIFE.. THANK YOU SO MUCH

[@profrobbob]

I figured that, and yes ln(e^3) is 3 because the like bases of e cancel.

[@xavierserna]

Nice job. You are a great teacher! Keep doing what you do man!

[@PythonDelta]

SUBBED! Great job. Awesome hand writing as well, sir!

[@profrobbob]

+PythonDelta thanks for watching, liking and subbing! If you need a break from math I have a video teaching my cursive too...lol

[@juliecramer7768]

ProfRobBob Great! I just told one of my kids I wished I wrote like you.

[@profrobbob]

You are VERY WELCOME:) I am glad I could help.

[@professorrice5470]

I have my final exam tomorrow, and you really did a great jop explaining things about logarithms. 100 thumbs up from me!! God bless you..thank you for helping me understand this better. Ps. You teach and discuss better than my Math Teacher. Hahaha.. #ProfRobBobTheBest

[@professorrice5470]

*job not jop. Sorry typo.

[@profrobbob]

You are very welcome!!! I hope you did well on your test:)

[@bubudoo11]

Great explanations, thanks!! Really helpful video, so glad I found your channel, my exam is in 4 days! Just in time!

[@debasissahu5261]

Sir, when you jump around u look much friendly. Thanks!!!!! I am blessed.

[@profrobbob]

You're welcome Debasis Sahu and thanks for choosing my channel to learn from!