solving a nested logarithmic equation

0:00 log equation battle log(x)+ln(x)=1 vs log(x+ln(x))=1
5:00 check out Brilliant

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[oxygen]

Meanwhile in another universe:
Wambert L function

[Rizwanalam]

You've succinctly explained the intricacies of logarithm. Thanks.

[chessematics]

The first could be further simplified to 10^(1/(1+ln10))

[fantiscious]

I wonder if there's a simplification of W(eˣ), since e^W(x) is the reverse function composition of it and is equal to x/W(x)

[slytherinbrian]

I've watched so many of these videos that the second equation with the Lambert W Function was easier for me to solve than the first one!

[anuragguptamr.i.i.t.]

Please explain us the trick, concept and proof of converting definite integral into summation and vice-versa.

[varun]

Logarithms are awesome they help to solve equations involving complicated powers, but even more cooler are the complex numbers.

[iWilburnYou]

If we start with an equation of the form

where a1, a2, ..., an are positive integers and c is a real number,
=>
=>
=> log(x)*sum(1/log(ak), k, 1, n)=c
=> log(x)=c/sum(1/log(ak), k, 1, n)
=> x=10^(c/sum(1/log(ak), k, 1, n))

[BeckBeckGo]

My brain processes speech slowly. And you sir, slowed down, are majestic.

[Christian_Martel]

At school, I’ve also learn that log(x) was in base 10. I was a bit confused when I use WolframAlpha for the first time and that they use log(x) as in base e.

[mariogalanguerrero]

Bprp what about a video on how to aproximate values of lambert W function?

[blakedylanmusic]

By change of base again, 1/ln10 = lne/ln10 = loge so we could simplify the first answer to x = e^(1/(1+loge))

[pranavabharadwaj]

Not a usual viewer, but this is helping. Thanks

[wuyqrbt]

Nice and thank you dear Teacher .
Teacher, please make videos including with Matrices.... Please 🙏
*bP🖋️rP🖍️* .... 💗

[limitless]

Can you help me solving this
dx/5sin(x)-4cos(x)

[leonardobarrera]

Hello people, this man is called
But is true, I have seen in his other channel, where he has photos with Cliff, in the last photo, it say for Steve

[fibroidss]

that's cool but PLEASE PLEAS do not forget to restrict the domain to where those logs ar definde please!

[nocturnalvisionmusic]

*_Don't you love it when logarithms battle it out? >:D_*

Sorry that's the first thing I thought from this title >~<
Thank you for another wonderful video bprp! ^w^

[majkgmajkg]

wow, got both :o although I'm pretty skillful in math, it wouldn't be possible without following you for couple last years. nice! <3

[moeberry]

Good video but you should explain that there is only one solution since e^10> -1/e and less than 0. So there are not multiple solutions. It must be stated since this is a multi valued function.