Change of Base Theorem is used to solve this equation.
Пікірлер: 84
@InteligentToast7 ай бұрын
brilliant! i loved logarithmic equations in school, but we never learned to solve an equation with different bases. thank you!
@kimabrams977 ай бұрын
I’m going back to school at 42 for electrical engineering and your videos have helped me immensely. Thank you!
@MonicaMLBH7 ай бұрын
Good for you. Congratulations!
@MonicaMLBH7 ай бұрын
Very admirable!
@BroadwayNPO7 ай бұрын
Same! Best of luck!
@wileynicholson16827 ай бұрын
Bless You. I walked into LSU at 30 years old (Chemical Engineering) Most of my classmates thought I was the Professor.
@robertcampomizzi79887 ай бұрын
I'm your age... My Brother was E. ENG and my Dad was in Chem. Eng. I'm going back and (re)- learning. This guy has great vids. You're absolutely right.
@samuelkelly21976 ай бұрын
Mr H is just FANTASTIC. He has sent me back to the 70s and I would love to keep pace with him. He makes Mathematics FUN. Straight to the point but we would sometimes like to have some tit bits from him and to introduce some books for us to acquire, without promoting others too much if he has some books or Pamphlets on Logarithms and Indices and Trig and Calculus, some of us would love to acquire them. Thanks Sir. We love you Mr H.
@thomasrogers82397 ай бұрын
I am always blown away when I learn more about logarithms
@doyourbest76557 ай бұрын
Perfect explanation!
@luisclementeortegasegovia86037 ай бұрын
Very useful professor 👍
@bawatabetando69026 ай бұрын
I am going back to the benches at 68 to complete my MD degree. I am also greatful for these scirnce videos.
@ToTheWolves5 ай бұрын
Congrats! I’m about start a second bachelors in physics after 20 years.
@88kgs5 ай бұрын
@@ToTheWolvesall the best 👍
@88kgs5 ай бұрын
All the best 👍
@zanonoza49184 ай бұрын
Love hearing that ❤
@ToTheWolves4 ай бұрын
@@88kgs ty
@onyedikachi.godplssaveourg77693 ай бұрын
Thank you sir, please keep it up
@newoap7 ай бұрын
Making maths beautiful. Thank you sir. 🙏
@mrhtutoring7 ай бұрын
Thank you for the nice comment.
@chimaths-class7 ай бұрын
Great job🎉
@jeffroberts9302 ай бұрын
Good stuff. Thank you.
@hassanadan31157 ай бұрын
Good keep up.
@user-ky5dy5hl4dАй бұрын
Splendid.
@BruceLee-io9by4 ай бұрын
Very clear! You are a great teacher! Compliments!
@georgesadler78307 ай бұрын
Thank you for the video.
@devondevon43667 ай бұрын
Answer x = 8. 359 A different approach. Log 2 (x) + Log 3 (x) = 5 This means: 2 raised to a number = x added to 3 raised to a number also =x and the sum of these = 5. let p = the number 2 is raised to; let n= the number 3 is raised to; Hence p + n =5, and hence, n= 5-p, So: 2^p = x, and 3^ 5-p = x Hence, 2^p = 3^5-p (since both = x, transitive property, if x=y and r=y, then x=r) log (2^p) = log (3^5-p) ( log both sides) p log 2 = (5-p) log 3 (rules of log) p = (5-p) log 3/log 2 p = (5-p) 1.58696250072 p = 7.92481250361 - 1.58696250072 p p + 1.5869p = 7.9248.. 2.58696 p = 7.92848 p = 7.9248/ 2.58696 p = 3.0633658 recall x = 2^p and we are solving for x , hence, x = 2^ 3.0633658 = 8.359 answer Verifying if 8.359 is correct note that since p = 3.0633658 then 5-p = 5- 3.0633658 = 1.9366342 and recall x also = 3^ 5-p = 3^ 1.9366242 which also = 8.359 p
@kimutaiboit85166 ай бұрын
Yours is much easier to follow. ❤
@Chewy4275 ай бұрын
not a pure answer, ew
@JulesMoyaert_photo7 ай бұрын
Thanks!
@justabunga17 ай бұрын
If calculators aren't allowed and by looking at the second step, then we can find the LCD, which is log(2)log(3). Multiply everything by that LCD, which is (log(3)+log(2))log(x)=5log(2)log(3). Divide both sides by log(6) (from log(3)+log(2)), which is log(x)=5log(2)log(3)/log(6). There are 4 acceptable answers for solving for x, which are x=32^(log_6(3)) or 3^(log_6(32)) and 243^(log_6(2)) or 2^(log_6(243)).
@cret8597 ай бұрын
If calculators aren't allowed, I hope that logarithm tables are ! In this case, the best way is to transform the initial equation in order to get an expression with any logarithms you may find in the available tables. If no table is provided (or allowed) then your last hope is to graphically hint for the solution on a sheet of logarithmic millimeter graph paper.
@rleroygordon7 ай бұрын
I don't really spend much time with math any more but I'm still interested in the subject. One of the things you can do to work problems like this, if you aren't allowed a calculator, is to spend a little time making up a mental toolbox of powers and roots, and logarithms of primes. It takes a little time to do the memorization, and you'll have to keep reviewing occasionally to refresh your memory, but it makes this much easier.
@gregnixon12965 ай бұрын
At the beginning of the video, I thought the solution would go in the direction of the LCD, and we would leave the calculator in the drawer.
@bibekanandhakirttania75242 ай бұрын
Thanks for the vedio
@jan-willemreens90107 ай бұрын
... Good day to you, One short remark regarding approximation, maybe it would be better to approximate X at the very end of the algebraic calculation, instead of approximating 1/log2 + 1/log3 (5.42) and then again with 10^(5/5.42) ... obtaining less accuracy? Thank you for your math efforts ... happy weekend, Jan-W
@mrhtutoring7 ай бұрын
Thank you for pointing that out. I thought about keeping the exponent as 1/log2 + 1/log3 as well. I calculated the final value with 1/log2 + 1/log3 as the exponent and also 5.42 before making the video. Difference between two was very minimal.
@jan-willemreens90107 ай бұрын
@@mrhtutoring I made that remark because of my technical background (lol) and thanking you for your clear explanation ... take care, Jan-W
@jackelliott42622 ай бұрын
Dude thank you so much 😊 your the best man!
@jackelliott4262Ай бұрын
Yoooo thank you I got an A- after failing 3 tests back to back and studying 4 hrs each thank you bro
@mrhtutoringАй бұрын
Good job!
@jackelliott4262Ай бұрын
Btw would you consider making a video on circles, ellipses, parabolas, and hyperparabolas.
@mrhtutoringАй бұрын
I will try~
@SAMIRKHAN-jk2rq7 ай бұрын
Magnificent
@z0ru4_7 ай бұрын
With the exact values, it would round up to 3.373
@Chewy4275 ай бұрын
x = e^(5 ln 2 ln 3 / ln 6) looks cleanest
@publicutility7 ай бұрын
🎯🏆🏁
@maxime96367 ай бұрын
👍❤🙏🙏🙏
@KaiCulture7 ай бұрын
Can you do derivatives and intagration and sigma rule ❤
@zanonoza49184 ай бұрын
Am asking for the same here 😊.
@luisclementeortegasegovia86037 ай бұрын
Proffesor, how come you prefer ln to log?
@mrhtutoring7 ай бұрын
2 letters vs 3 letters
@triple_gem_shining7 ай бұрын
Lol!
@88kgs5 ай бұрын
@mrhtutoring 😊😊
@annshephard39292 ай бұрын
5.4178313691767469521668869515108 and 8.3658336590275351036590017462244 to be more exact. I had to do the math. :D
@xinanipoh7 ай бұрын
One simple question...when do we need to use this logarithm equation on our daily life or real life situation?
@TranquilSeaOfMath7 ай бұрын
It depends on your situation. You probably experience it and don't know it. The decibel scale and the Richter scale are both logarithmic.
@triple_gem_shining7 ай бұрын
Logarithmic equations are used a ton for scientific calculations. One example is chemistry ( which im studying)
@triple_gem_shining7 ай бұрын
pH (concentration of hydrogen cations) is also logarithmic..
@carultch6 ай бұрын
This exact example, unlikely. Logs in general, they have plenty of applications. Some examples I can contribute: 1. Cooling and heating, and predicting the time for heat to transfer. To invert the exponential decay function that tells temperature vs time, you use logs to do so. 2. Decibel and octave scales, that translate frequency and intensity into a form people can understand as pitch on the music scale and the decibel scale for sound level. Human hearing is logarithmic in nature. 3. Electrical timer circuits. Electrical timer circuits, use an exponential decaying signal to keep track of time. The resistor-capacitor charge/discharge behavior is an exponential decay. To invert it and determine time, you'll use a logarithm function.
@88kgs5 ай бұрын
@@carultchthanks for the answer 🙏
@seekingCK5 ай бұрын
Sadly in my Country we dont plug the log into the calculator :(
@ureditor_stay7 ай бұрын
wait so will the value always be 10? ( here, 3:12 ) or is there a condition??
@curiousobserver53816 ай бұрын
It is the base of the logarithm used to unify the bases. In this example decimal log was used, so both sides were raised as exponents of base 10 in order to get x on the left side. You could use ln - natural logarithm to replace log2 and log5, and in that case you would use e instead of 10 here.
@carultch6 ай бұрын
Depends on context, and on the rules of your calculator. The short answer is that it is most common for log(x) to mean log base 10 of x by default. Most scientific calculators and Google Calculator use this convention. In pure math, the notation is also used for log base e. Ln(x) would mean the real numbered logarithm function, while log(z) would be the complex log. Log base e is preferred in pure math, because its calculus is the most elegant. Wolfram Alpha uses this meaning of the log function, so you have to rename it to ln(x) when copying it to other programs. Less common is for log without a specified base, to mean log base 2. Commonly preferred in computer science applications, though I'm not aware of any software meant for the general public that uses this convention.
@luisoswaldoramirezzevallos30496 ай бұрын
I like You matter
@Tharr_bang7 ай бұрын
Can someone tell me where the 10 comes from😭
@jan-willemreens90107 ай бұрын
... LOG(X) means LOG(base 10)(X), so suppose LOG(X) = LOG(base 10)(X) = 5 , this means that X = 10^5 ... LOG(X) doesn't show its base 10 ... hope this helps you ... Jan-W
@Tharr_bang7 ай бұрын
@@jan-willemreens9010 thanks alot
@IRoXXI7 ай бұрын
the expression "Log" without an explicit base is defined as Log to the base of 10. In this example he just took the second equation where he can substitute the log of b to the base of a on the one hand and the division of log of b to the base of c and the log of a to the base of c on the other hand. C is not defined so he could use any base. He chose to use the base of 10 though he said he would prefer the log to the base of e (ln).
@abdulaimsheriff19377 ай бұрын
Logx is in base 10
@triple_gem_shining7 ай бұрын
Log (no base) is assumed to be ten
@nathansodja5 ай бұрын
And that's why I hated Maths, keeping track of all the different principles
@tyscott49495 ай бұрын
I got sad when he solved the rest of the problem with a calculator.
@samuelmarquardt78843 ай бұрын
stop rounding answers!
@mrhtutoring3 ай бұрын
Can you not round a log answer?
@70subswithoutanyvideo137 ай бұрын
Great ❤
@chinchang5117Ай бұрын
I believe we should use 5.417831369177, instead of just 5.42. Because we need the final answer to be 3 sig fig.