Change of Base, Logarithm

[@AnnieMatipa]

Much appreciated sir surely goodness and mercy shall follow you all the days of your life

[@dixonwalker]

Your channel is really helpful , keep up the good work, Mr sichamba

[@manassehmusonga9259]

Wonderful teacher let's get this man to 2.2m subscribers, all the best sir.

[@JohnSmith-hr7fl]

You could have done it very simply. For Logarithms, you can raise the base of any logarithm to any power you like, as long as you raise its argument to the same power as well. So, you could have squared log2^x, to get log4^x^2, then you combine the logs to get log4^x^3, then put it in exponential form, so you have 4^6 = x^3, then of course take the cubic root, so 4096 cube rooted, to find that x = 16.

[@MillicentWiredu-d8p]

You're right boss

[@UnclePythagoras]

Big up sir Jacob you have it in you I wish you all the best the world needs your light ❤

[@BewTheAtom]

From 6:15 onwards, he changed from logarithmic form to index form. Log2^x=b(logarithmic form) == x=2^b(index from)

[@JeanCyiza]

You're good teacher Keep going Jacob

[@jamesbamboo1755]

If you simplify the power of 2,the answer is 4. log base 2 of 4 is 2 then 2x6=12 divided by 1+ log base 2 of 4=1+2=3. Making the power equal to 12÷3=4!

[@WanabrianSavale]

Thank you sir for the lessons they really help ❤❤

[@ZealousSaidy]

Thanks sir for your help , I appreciate the Lord for your knowledge you're sharing with us 🎉

[@funlearningmathswithmr.a6988]

Perfect, way to go. Thanks Mr. Jacob.

[@RyanJoseph-d4o]

It's very awesome

[@edwinmwenda-q1e]

It is really helpful sir.

[@deepreacher]

You don't have to punch a calculator to determine the final value of "x". It can still be simplified further to give same answer. Thanks

[@damarismutiso-dx2xo]

Evaluate this for me please l log x + log x cubed minus log x squared is equals to log 100

[@Seaclock24]

Bros been waiiugtin​@@damarismutiso-dx2xo

[@ShangoshiwaProtasio]

This vedio is really helpful thanks

[@CollenChigama]

Very helpful Mr Sichamba J❤

[@WhyfordKhondowe]

,thank you very much ,continue helping us

[@Omddw2024]

Yeah, I agree with most if the comments. Could have simplified the logs earlier to make the equation easier to work with. But well done. I won't fight your approach since you maintained the accuracy of your soln

[@samueladler9080]

Very impressive but log x base 4=½log x base 2 Log x ¹`². x base 2=6 By exponentiating we have x³'²=2^6 By inverting the exponent 3/2 and multiply both exponents by 2/3,we have X=2⁴=16

[@suleimanadamuumar7395]

Thanks you sir I hav (learned) a lot from your lesson

[@KUTLWISANOBALALA]

excellent work sir

[@nandakumarcheiro]

Answer as x-16 can be brought out. Answer is correct.

[@Seaclock24]

DAYUMN DIS IS G LIKE TEACH

[@peterkatongo6797]

Thank you sir

[@akolmadingakeen8337]

Thank you so much, Teacher ❤😊

[@Burningarrow7]

I'm new to logs and I've solved this equation 3 different ways that were much simpler and easier. You might want to simplify your methods for your students as to not over complicate their lives unnecessarily

[@BettyNdesh]

I really do understand much appreciated

[@Abouhydar]

This method is not meant for beginners. There so many ways of solving in little steps.

[@SaningoKipasi]

It's woow

[@pascalmutinda2282]

Good stuff

[@benardnzuki-v8s]

At the last step it can be solved without even the calculator, Mr tutor

[@gesaalpa6620]

Good job thanks

[@JacobLasu]

I'm really getting the knowledge

[@ckmedia8285]

this was so helpful to me

[@FillemonSimon-m6j]

Fantastic

[@creativeartwow]

Is the factorization correct??

[@shawn-the-first.1643]

❤❤❤

[@kelechidanielikeh2153]

Thanks Sir

[@MosesKatongo-r4g]

Thank for the help Sir

[@richardkapalu2711]

Are you sure the factorization is correctly applied there

[@jamesbamboo1755]

Very correctly applied Sir/madam whatever the case may be.

[@PanganiHaruniTimotheo]

Thank you for good work, but the final stage to the answer is easy to simplify and get the answer, so I advise not to use a calculator for solving without using the calculator is most preferable.

[@WameLesianang]

I didn't get how u multiplied to remove the denominator

[@abioyebolanle7911]

Pls sir solve loga 27+ logb 4 = 5

[@AbednegoKamwea-mo6jg]

Hello. ..a little bit confused... because of two unknowns

[@AmoabengGodfred-f2g]

More sir Thank you

[@brownchama6330]

Thanks sir

[@GodrickOtwani-s6t]

Thanks sir its best

[@Graceoseghale-d6z]

This video is really helpful God bless you sir

[@EliatoshaMbogo]

You are doing well but you go fast

[@ssentongopaul9160]

Mr next week we r doing final exams buh man am scared

[@JamesKago-d5d]

How is paper two am really scared

[@gideonganyo1457]

Sir please the solution is not clear

[@RandyRandy-bg5wz]

Good teacher

[@EstherNakaye]

Thank you very many sir

[@AA-pf6ed]

How?

[@adgf1x]

=>1/2log 2 basex +logxbase2=6=>3/2(logx base2)=6=>logxbase2=4=>x=16 ans

[@rosemarysampson8992]

Wow

[@tohidurpurkait6844]

This is long method for students understanding , so you have to solve it shortest way , my answer also 16 but 3 line solving tricks

[@oluwajuwons08gmail]

Kindly share pls

[@adgf1x]

log x base2=6×2/3=4=>x=2^4=16 ans

[@oahuhawaii2141]

You made the problem too messy to do because you failed to realize that log2(4) = log2(2²) = 2 . This means at 02:45, you could write: log2(x)/2 + log2(x) = 6 log2(x)*(1/2 + 1) = 6 log2(x)*3/2 = 6 log2(x) = 4 x = 2⁴ = 16 Why use a calculator?

[@jamesbamboo1755]

Yes, but that's just another method...nothing messy about it. Maths is a mental subject that trains the mind to solve problems and believe you me, a single problem can be solved using several different methods!

[@harrymatabal8448]

Log x base 4=(log x)/(log 4. Log 4=log 2^2=2log 2 (Log x)/(2log 2) +(Log x)/(Log 2) = 6

[@harrymatabal8448]

Multiply by 2log 2 Log x + 2log x =6 ×2log 2 ÷2 Log x + log x = 6 log 2 2log x = 6 log 2 ÷2 Log x = 3log 2 =log 8 x = 8

[@oahuhawaii2141]

@harrymatabal8448: line 2 is correct, but line 3 is wrong. Fix it with: log2(x) + 2*log2(x) =6*2*log2(2) 3*log2(x) = 12*1 log2(x) = 4 x = 2⁴ = 16

[@HakimAdamKuku-cg6pd]

We are just fellow your platform , therefore we short format otherwise am lose

[@moureenkatumba7956]

Thank u sir 🎉

[@TukeiSimon]

More sir❤

[@adgf1x]

3/2 log xbase2=6=>logxbase2=4=>x=16ans

[@mutintapuritysiasokwe2686]

do you teach science?

[@EstherNakaye]

Can't we solve it without saying that x=2^others

[@jagadiswarchakraborty295]

The base of the first term is 4 which is 2^2. Just bring this exponent 2 as 1/2 infront of the first term and then the base is the same of both the term. Then the solution is readily there which is 16.

[@kashendamusole]

Am not understanding on changing the Base

[@solomonmuturi6969]

Just explain how you got 16 with better clarity

[@adgf1x]

logxbase2=6×2/3=4=>x=2^4=16ans

[@lezamrombo1699]

You don't have to use a calculator here sir.

[@walusimbisudais208]

Thank u so much 🙏🙏🙏🥹

[@kalid-x4i]

❤

[@NakibuuleAnnTracyWaldah]

You have made a mistake on the second step

[@BrianOmondi-z6g]

What is the mistake he made

[@DafrozaMkongwa]

Duh thanks so much Mr

[@ANDREWMWANGI-j6g]

....😵‍💫😵‍💫🤯

[@machekebarac6607]

Thanks

[@adeyinkaadigun5406]

U shud b able to simplify further to get 16 without using calculator

[@Jellyenossurup]

Please Mr.explain in short form

[@titustarhemba4678]

Somehow confusing Sir.

[@GraceNakiyaga]

I have apricoated

[@olayinkabalogun243]

Sir so sorry to say but i thank you feel like writing , there is too much of mess sir pleas kindly review your work

[@prollysine]

x=e^(6*ln4*ln2/(ln4+ln2)) , x=16 , test , log₄16=2 , log₂16=4 , 2+4=6 , OK ,

[@EdithWilo-le7ut]

Which grade is this topic coming from sir

[@jacobsichambaonlinemath5090]

It's general

[@EdithWilo-le7ut]

Okay

[@peterkatongo6797]

In additional mathematics grade 12

[@peterkatongo6797]

In additional mathematics grade 12

[@conchfrittersoup]

uh oh

[@johnake2454]

This method is unnecessarily too long. You can solve this problem in an easier and shorter way

[@harrymatabal8448]

No need to remind us about the rules. We are not stupid.

[@mesagnaamepaulus7957]

Why are you so rude bathwetu 😢??

[@savasalpdo]

right ,but bad solution

[@EdwardDzorvakpor]

Please I don't understand

[@FentingMicheal]

I don't understand

[@oahuhawaii2141]

log4(x) + log2(x) = 6 log(x)/log(4) + log(x)/log(2) = 6 log(x)/(2*log(2)) + log(x)/log(2) = 6 log(x) + 2*log(x) = 12*log(2) log(x) = log(16) x = 16

[@NicolusRono]

Long

[@johnchiya3814]

You have made a mistake sir kindly review yo wrk

[@tshepomohotwane7466]

That's true

[@tshepomohotwane7466]

Didn't he leave 1

[@Myth-Mirage]

@@tshepomohotwane7466 No it's the correct answer.1+log4/2 Is equal to log2/2 +log4/2(log a/a=1). 1 in the 1+log4/2 is replaced with log 2/2 to make the bases equal .so then log2/2 +log4/2 in equal to log 4*2 /2that is log8/2. 8 is 2cube.therefore log8/2 is equal to 3log2/2 that is equal to 3(log2/2 equals 1.1multiplied by 3is 3.now denominator is 3.we have 6 in the numerator which cancels of as 2.(Because 6/3 equals 2).now log4/2 ×2 .(4 equals 2 square) now log4/2 is log2square /2,now the square comes to log .now it becomes 2log2/2 ,this equals 2.now 2multiplied 2equals 4.therefore 2raised to 4is 16. Hope that clears your doubt

[@leninbarathi6531]

Where

[@henshelkasonde3920]

No it's the correct answer but that's not how they solve in a case where there is no a calculator

[@adgf1x]

replace log4base2 by2

[@oigonathan]

kzbin.info/www/bejne/j2K7Y2Snqahkb9ksi=yY5OekcndgcPIQxh

[@MessyKerry]

Not clear

[@AmoloJoshua]

So long

[@krishvignesh5898]

thank you so much sir

[@SundayAgboola-f2p]

Sir you made a mistake

[@JohnnyThrill-nu2ro]

Sir sorry to say but I think you feel like writing, ahhh this is too much of a mess

[@AndrettiEzigbo]

I can't understand shit