Logarithms Review - Exponential Form - Graphing Functions & Solving Equations - Algebra

This algebra 2 & precalculus video tutorial shows you how to evaluate a logarithm without a calculator, how to simplify logarithmic expressions, how to expand a logarithmic with a radical or a square root, how to condense or compress a sum or difference of logs into a single logarithm.
Domain and Range Formula Sheet:
bit.ly/4eheN2W
Logarithms - The Easy Way!
• Logarithms - The Easy ...
Log to Exponential Form:
• Writing Logarithmic Eq...
Change of Base Formula:
• Change of Base Formula...
Change of Base Log Problem:
• Logarithms
Properties of Logarithms:
• Properties of Logarithms
____________________________________
Expanding Logarithmic Expressions:
• Expanding Logarithmic ...
Condensing Logarithmic Expressions:
• Condensing Logarithmic...
Natural Logarithms:
• Natural Logarithms
Solving Exponential Equations:
• Solving Exponential Eq...
Exponential Equations - Quadratic Form:
• Solving Exponential Eq...
_______________________________________
Solving Logarithmic Equations:
• Solving Logarithmic Eq...
Graphing Logarithmic Functions:
• Graphing Logarithmic F...
Graphing Exponential Functions:
• How To Graph Exponenti...
Compound Interest Word Problems:
• Compound Interest
Logarithms Practice Problems:
• Logarithms - Practice ...
_______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Logarithmic Formula Sheet:
bit.ly/4fEwqv0

[@TheOrganicChemistryTutor]

Domain and Range Formula Sheet: bit.ly/4eheN2W Logarithmic Formula Sheet: bit.ly/4fEwqv0 Final Exams and Video Playlists: www.video-tutor.net/

[@jedrzejbielawiec5658]

With the help of this channel I was able to pass an electronics test to advance to a higher position at the company I work for. I decided to go back to school recently and do all my classes remotely because I work full time. This man is about to help me get through my pre-calculus class. You should be a professor, your teaching style is absolutely phenomenal and so easy to understand. I cannot thank you enough for everything this channel has done for me. Please keep this up!

[@jeffreyyuan8663]

this dude should change his channel name to "The STEM Tutor"

[@Green-r8n]

But previous name is popular from east to west now

[@elizabethcaballero4160]

these videos are VERY helpful! they make it easier for me to understand step-by-step. thank you

[@mohamedkass3885]

Thank you, you are a life saver 🙂

[@aroosaamjad4356]

Can someone tell that where we should appy log & where to apply ln? Or if it's okay if we apply any of them?

[@jimideux]

with this video, there's no way I won't Ace my next test.

[@John-bq1lp]

double negative = positive

[@zubayirhkazi9115]

John ikr...

[@insite8803]

Now this is how math should be taught to those who seek help in it, The Organic Chemistry Tutor goes through every possible scenario making it easy to tackle anything without the need of surprise.

[@jowo8862]

Disagree, a lot of questions in my honors class are still very hard and require you to think very conceptually. I feel like the should focus on problems like this too

[@extremebeastreaction6245]

@@jowo8862like the example problem is easy and then on the test they give something totally different

[@patrickdhatt3129]

20:07 Change of Base Formula 22:50 Convert to logarithmic form 25:05 Change to exponential form 25:59 Solving Logarithmic Equations 47:50 Graphing Start

[@prequelanimations539]

carefully hes a hero

[@Haru-eb3si]

you are the best 🥺✨

[@tjdeguzman803]

Okay, thank you ehe

[@s.h.1991]

Thx

[@daniaasaad9565]

king

[@jasonlinch4819]

Preparing to go back to school for my electrical engineering degree. Have been out of school for 20 years. Was solid on my math skills in '96. Thought I forgot a lot of it. Thank you so much for these videos. They refreshed and triggered so much of what I was not very confident about. Cant say thank you enough. Now I am confident that I can place well with the math entry exam they are going to make me take since my ACT scores are apparently too old for the school.

[@brickstv3156]

good luck i going gor mine to

[@HellloBianca]

Did you finish you engineering program? I'm happy for you! I'm embarking on a mechanical engineering degree, just finishing up some pre reqs right now.

[@strellagium]

please update us!

[@MainulWasTaken]

Current status?!!!

[@33nvyy_]

how are you doing??

[@ashleyoccelli4272]

12:22 is 2logx+ 3logy+4logz because those are all being multiplied :) great video though

[@MK-zy5re]

Ashley Occelli thank you! I was watching and saw that and cane to the comments to make sure :)

[@nancybaib5635]

Thanks

[@lesegolephoro1305]

had to pause too n check

[@Samurai-ub6ew]

Thanks I was wondering where the minus came from

[@gumZ-ne4ru]

I came to comment section to ask this but u already did it. Tnx

[@bababooeybababooey]

Your voice in all your videos is in a super low volume compared to any other video and music so I really have to crank my headphones up. So when you coughed at 43:29 I had some vietnam ptsd

[@happyfeet7123]

💀

[@pranavm.9513]

i thought the vietnam said vitamin

[@professional_silent_trumpe1540]

lmao, yeah that scared the shit outta me too

[@nikkyyxo]

@@pranavm.9513 same hehe

[@louzocco2162]

this video was probably the most helpful thing I've found for logs in precalc. absolutely amazing.

[@MT-nh5eg]

Did you win, son?

[@elhomie5666]

6 years later and this comment still holds true

[@elhomie5666]

6 years later and this comment still holds true

[@llo2861]

You are legit a genius, everything I learned makes so much sense now. Thank you so much!! You don't even know how helpful this video was.

[@TheOrganicChemistryTutor]

I still have a lot to learn.

[@uzzairhadefabdulhalim8962]

@@TheOrganicChemistryTutor You are a literal lifesaver for all of my matriculation subjects

[@tanneicabenjamin5447]

@@TheOrganicChemistryTutor We all do but you have taught us all so much. Thank you

[@niktaa5859]

I’m surviving IB math and chem because of him, thank you sm😭❤️

[@erongorani7207]

ur not alone:)

[@boipelomalahlela5577]

I totally agree with you.

[@eyespikes843]

Sounds like true hell LOL

[@Boobienoobie147]

Great tutorial. But his voice is too soft and soothing. It makes me want to sleep especially with the all black background in a dark room at 10pm...just before a math test in the morning

[@battleaxesam6042]

lol

[@amandasotolongo1994]

literally my not even kidding

[@tanneicabenjamin5447]

Agreed but he's still doing an amazing job

[@Pharomid]

Even with this great video i'm not so sure I can pass my Algebra 2 test tomorrow, the teacher's tests are insane. I'll try though

[@hermanosponce9996]

update? i know this was 2 years ago, but curious on how you did lol

[@Pharomid]

@@hermanosponce9996 it's been so long that I'm not too sure but if im not mistaken this is one of the only tests I did pretty good on. Thanks for asking :)

[@jowo8862]

@@Pharomid Having the same problem as you. You see, I'm doing an honors class which is really vigorous at our school. the average is like a 70%. the questions are really hard and conceptual so you gotta know the topic in and out lol

[@theodd1soout]

Half of the people in this comment have stopped learning by now some are dead some are lost souls some are rich and don't even remember it

[@harigopaladamus9481]

when a ramndom man on youtube is better than a teacher who studied for years to get their career

[@flatlanderjace]

2 hours to save the semester.

[@yoericz]

Relatable asf 😂 hope you were able to save the semester lol

[@firefoxx6185]

at 12:36 did you meant + 4log z, not -4log z, there was no division

[@imanhaji7166]

I think he is a slave of almighty sent to his people to help in order to be happy ,my allah bless of him he deserve more for me. you are the Teacher of Teachers(NO discussion) and you will be number one in all times.

[@johnathonstewart6666]

Iman haji Allaaaaaaahu Akbar

[@mr.incognito9195]

All of your material has been extremely helpful. In an hour and a half this video covered a whole chapter i had to read which would have taken me days. I appreciate the videos. i would be failing my class without them for sure

[@ascovers5132]

I've been sitting here laughing at 43:30 for the last minute. Sounds like a car trying to start up. Great video!

[@yongjwang]

12:37 Isn't it + 4logz?

[@grammar598]

yeah I think so

[@saedisaga7860]

yeah ,u are right ,it is+ instead of minus.........but we watched a fruitful video...thnks

[@faithachieng2935]

I also thought so

[@REALSLIK]

scrolled down to see if anyone noticed

[@chrispark6248]

@@REALSLIK same here

[@michelmanigat6322]

Excellent work. Clear demonstration. In one word: Perfect!

[@foixjonwilliamson]

who knew that mark wahlburg was so good a math

[@jess.7155]

I love your voice its so calming and helps me understand math (which i really, really hate) better. You don't go to fast and actually explain stuff in a way that is understandable to those who are not so good at math. I use your videos for each chapter in my Intermediate algebra class to understand it better. Thank you!!

[@Sultan_A]

🌟 Very Good, Long Teaching Problems, Keep It Up! 🌟

[@Jrockilla137]

33:05 lol I love it, I sat there for a moment trying to factor in my head as well, my first choice was completing the square on this one.

[@KennyyD]

I had to review this for my Calc class since I've completely forgotten logs from HS. Thank you! Now I can conquer the derivatives.

[@nimahanna1709]

13:42 you can’t subtract R from Z as they were multiplied together from one term. Brackets and factor out a negative.

[@ShenMantiquilla-fw5vz]

Struggled these topics for a month, then solved by an hour long lesson TT_TT

[@mattman3884]

12:35 I don't get why we put a negative sign infront of 4 log z shouldn't it also be addition?

[@RodgersLagat]

You are amazing sir..Your explanations are always the best❤

[@fallenazrael5291]

You just saved me sir. Just a few things happened and I wasn't able to watch my video lessons for the whole unit. I have a test at 8 30, i havent gotten sleep and everything is fucked up. U just sees saved my grade. Thank you very much

[@jacobm7026]

Just about everything was great! Good job! You made a minor error at the end relating to exponential decay or growth. Specifically, y = 2^(.5x) is still growth, albeit more slowly than 2^x. Just see how the function increases as you increase x.

[@grammar598]

this legit saved my grade, you came through for my ap chem class and you came through again for my pre calc class thank you!!

[@fernplays2494]

this video is legendary. Great work and I apreciate your effort alot. My math teacher doesnt have any patience but this really helped because i could do it at my own pace.

[@CHEAREEN]

I’m back in school after 20 years too. Was blocked by a student debt I couldn’t pay. Now that’s it’s paid, I’m back to finish my bachelors in math.

[@randomguy-hc7pv]

Wow you didn't give up..Im so proud of you

[@restyportacio5492]

At 12:33, why is the logZ^4 minus? Shouldn’t it be plus because it is multiplied together with X and Y

[@KL-ck2cd]

yes, its a mistake

[@zehra9600]

I CAN'T BELIEVE THIS. I'VE BEEN TRYING TO UNDERSTAND LOGARITHMIC AND EXPONENTIAL FUNCTIONS FOR LIKE 3 MONTHS AND I JUST DID! IM GOING TO CRY I LITERALLY MANAGED TO SOLVE MY HOMEWORK THANK YOU SO SO SO MUCH AND ALSO YOU LIT SAVED MY NEXT WEEK BEGINNING EXAM

[@d.o.t.4477]

OMG!!! I have a calc test on Monday and this dude just helped sooo much now I know I'm not gonna fail😂😂. This is probably THE most helpful video on logarithmic functions and graphing them. THANKS!!!!!!🔥🔥🔥

[@zamzammohamed8605]

You saved my life and ur voice is just 😍😍😍I could listen to him all day

[@llamallover1057]

I have my ap calc ab exam tomorrow and I realized I have no knowledge on logs, and the college board seems to love putting them in every other question. so I'm here now 😅

[@ibojofamily8472]

I don't know how you do it but I was able to digest everything at the pace you were going, which is a little fast for me but the way you explained everything and went through every possible situation allowed me to understand quickly. Life saver

[@arinkumar5406]

I wonder if organic chem tutor watches organic chem tutor videos to relearn a topic

[@cracked21]

He probably has notes from which he makes videos from.

[@imanhaji7166]

THis guy you can not compare any other Teacher for his capacity of all scientific subject such like chemistry,physics, and math. for his excellence we have admit, he is NUMBER ONE,NUMBER ONE,NUMBER ONE .Iam agraduate and I now how to evalute Teochers(well done)

[@dziedzormyaatugbah2030]

Amazing video.gonna subscribe right away 😍.And I just love the comments below 😂. great great job

[@k.c.9720]

I wish my god damn math professor explains his shit as clear as the organic chemistry tutor. I don't even want to call him professor anymore lmfao fucking suffocate us

[@blastwave1315]

I thank God because of you as one reason

[@komanemolefe107]

I think i got lost here: log(x^2 y^3 z^4) = 2logx + 3logy -4logz. Why -4logz ?

[@denvercharlebois699]

It should be 2logx+3logy+4logz.

[@despairbear3936]

I learn more from ten minutes of these videos than I do weeks of class

[@nickthe1million336]

1:18:31 absolutely phenomenal video, although I’m pretty sure y=2^0.5x is growth because it is essentially 2^1/2, which is square root of 2, a greater number than 1

[@Drewski777]

Math is so fricken cool! Like, THE COMPOUND INTEREST FORMULA LITERALLY BROUGHT US TO THE MOON AND HELPED CREATE THE ATOMIC BOMB BASICALLY?

[@MelisssaBai]

Question 12:22 Why is z négative?

[@IMathTutorial]

OK Thanks

[@xTriplexS]

12:36 should be 2logx + 3logy + 4logz. He probably made a small mistake. Happens.

[@firefoxx6185]

at 56:13 wouldn't it be (2,-∞), because (-∞, 2) would move from third to forth quadrant?

[@rossisempre86]

Why at 12:36 is the answer -4 log z and not just +4 log z..? This wasn't explained and doesn't seem right.

[@MsHortel]

I love this young man's soothing voice. It powerfully sets what he teaches in my brain❤ and Im a grandma.

[@champagnepapi_ovo]

12:16 you shouldn't substract z

[@exstand3029]

Thank you

[@oldsachem]

JG must use a calculator to approximate the square root of 2 because the square root of 2 is an irrational number which does nor terminate as a base-10 decimal.

[@alltooswift]

My precalc teacher was out for a week (not her fault, her mom was really sick) and we didn't exactly learn this unit, and the test is tomorrow... luckily I think I have a good grasp on logs now! Thank you

[@brax300]

43:50 “” try this problem, e to the *insert car trying to start noise* excuse me. “ fun laugh half way through this study

[@grdsinclairgrd]

it deserves 10^10000 algorithms. thank you, teacher.

[@ryanevans1408]

Really appreciate you man. You make things so easy to understand

[@jingjingliu411]

12:35 log(x^2y^3z^4) =log x^2+log y^3+log z^4 =2 log x+3 log y+*****(PLUS)4 log z no???

[@MarioFranco-lu3gl]

@41:45 when he's dividing, why is he putting the negative term at the top as the numerator? does anyone know?

[@sanopann1896]

7:12 why and how did it become 10 to the minus 3 idon't get that part and the rest example make no sense anymore

[@barakah08]

Why is it -4 log z at 12:35 ? Shouldn't we be adding and nit subtracting?

[@Haru-eb3si]

there is exactly one hour left for my exam and this helped alot many thanks 💖☺️

[@alvikolina1416]

You should be working at space x what are you doing here???

[@Vicseverin]

why did I take a semester of algebra when there is this video...

[@mayahfils1852]

You are amazing. Thank you for making my life easier. I learn more from your videos than the actual class.

[@FatsFalafel]

I appreciate the video but there are little mistakes here and there that make it confusing.

[@MsHortel]

Thank you Dearest Angelic SuperTutor. You have cured my math trauma. God bless you.❤❤❤ You are the reason I am at A in my math class hijo. God bless you billions times over. One day I froze and panicked bcoz I didnt how to answer the practice questions and I couldnt understand the book at all. The book was giving me migraine instead. So I knelt down and prayed to St. Joseph Cupertino. Then I started clicking on youtube and stumbled across your video and exactly the explanation I needed for the problems that gave me panick attack. Now I look at the name of the section of the book and come straight to your videos and attend your youtube lectures. Your videos is my math classroom😁😁😁🙏❤️🙏 Thank you so much.

[@kushgupta5787]

12:30 I think the U got the answer wrong as log z^4 = 4log z instead of -4log z

[@lilcurry4314]

12:45 hey man I’m pretty sure you’re supposed to add logz4

[@uhuhuhuwhauwhauwhaaha7918]

but log base -2 of -8 = 3 so negative values on logs sometimes make sense

[@franck777]

Not fraction, you mean lower than 1. 3/2 is a fraction.

[@faithisabel25]

Maraming Salamat (Thank you) for posting this video :-)

[@n1sha.ace33]

@@jamaljamal-nt5ke i thought so too

[@katl8go]

kzbin.info/www/bejne/paKre2iuhr6He6s the line does not touch the asymptote but it passes near to it.

[@Aplus612]

Some error I have seen while graphing 1:01:022

[@studywithme5998]

this vid was really helpful thnx but I have a question: at 1:12:27 if the question says it doubles every 20 min lets say what do we do in that case? will it be like y=5000(2)^t/20 or??

[@shainiaakoya8341]

Who are you? I been searching you every where.. you're a ghost but still saves my life everytime I have math problem.. Love you man❤❤❤❤❤❤❤ thanks alot

[@piyodsbl1900]

12:36 See, I don't get why the four had to have a negative in front of it? Where did it come from? It seems totally out of the blue, I mean the rest don't have a negative-- so, why does the four have one?

[@eshanths8652]

It’s a mistake it’s supposed to be + since they are all being multiplied.

[@mathewbjorklund2861]

12:36 Why was there no explanation on 4logZ being negative? was holding up so far, but that makes learning jarring.

[@mathewbjorklund2861]

add an annotation over it will help alot

[@queenkaine3619]

For graphing exponential if the function is y =x^2e^x, the horizontal asym is 0 I am saying if there’s no number adding to the function, the horizontal asym is always zero? But this video really helped me thank you sooo much 💯 I have a test coming next week and is hard understanding how to graph exponential and logarithm function but here I am finding the most understanding video Merci beaucoup from Montreal 😊😊

[@zenwi3068]

hey at 31:52 couldn't you just subtract the log to the other side. Then turn It into a division problem that = 0. Log2 (x^2+5x)/(x+4)=0?

[@anabilrahmangaming7622]

The problem you are solving at 45:22 .. is this even Algebra 2 or is this pre calculus? Cause my brain hurts now xD but somehow I understand it xD

[@betselotgetahun4805]

why -4logz at 12:35

[@eric.ismeee]

someone help me solve these simultaneous equations : 2^(x+2) + 3^(y-1)=7 and 6^x + 2^(x+y) =5(2^(y+1))

[@beachwave5705]

why are you subtracting 4logz? 12:37

[@frankkalobwe107]

For the range of exponential functions , you said it will start from the lowest value of y so in the example you gave y=2^x+1 -3 in the video you said the range is (-3,infinity) but won't the lowest value of y occur when x is 1 giving us 2^0=1 giving a y value of -2 as the lowest so which one is which?

[@robertkesselring]

Logs of negative numbers are well defined. For example, rearranging Euler's identity gives you have ln(-1) = i pi

[@autocad1948]

it's very helpful, i use my book only for exercices, thank you for all.

[@ashleyliu5776]

wow first time we get a problem that. cant be factored

[@justbrowsingthroughstuff2190]

"Try this problem, e to the *hmmm mhhh mhmm mhh mhh*" 😂had me