A Surprising Exponential Equation

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2^3^9^x=4^9^3^x
#ChallengingMathProblems #ExponentialEquations #Logarithms
via @YouTube @Apple @Desmos @NotabilityApp @googledocs @canva

SIMILAR PROBLEMS 🤩

PLAYLISTS 🎵 :

[viniciusdemoraes]

I like your sense of humor, thanks for the video :)

[chrisjuravich]

I have worked this problem earlier today, and I’m just now reviewing your video solution. Please post this video on Twitter, so that I can post my (different) solution.

Thank you, sir, for your continued service to the online mathematics community.

[Qermaq]

5:20 I used to work at a KMart (it's no longer there, as with most places I worked or went to school) and we would joke "the K stands for Kwality". This made me remember that, thanks.

[GreenMeansGOF]

Ln of a negative number is complex. Nonreal numbers deserve love too.

[kianushmaleki]

Homemade equations!

I love them. Please cook more equations 🙂

[supertimer]

when you substitute the final answer to the original equation, it shows that the solution is wrong. the flaw is at 1:39. The only solution is: x=0. btw, ln of neg is solvable.

[damiennortier]

Here's a crazy way : always log both sides
3^9^x*ln2 = 9^3^x*ln4
9^x*(ln3 + ln(ln2)) = 3^x*(ln9 + ln(ln4)
a last time :
x(ln9 + ln(ln3 + ln(ln2))) = x(ln3 + ln(ln9 + ln(ln4)))
Second : simplify
x(2ln3 + ln(ln3 + ln(ln2))) = x(ln3 + ln(2ln3 + ln(ln2) + ln2))
Third : put everything on the same sides and factor
x(2ln3 + ln(ln3 + ln(ln2)))/(ln3 + ln(2ln3 + ln(ln2) + ln2)) = 0
To make thinks more beautiful, les a = ln2 and b = ln3 (to be or not 2b)

x(2b + ln(b + ln(a)))/(b + ln(2b + ln(a) + a)) = 0

So, the last step can be forgotten 😁
From here, x = 0 🤔

[hunnus]

x=0 is also a solution right? Just because we can write this as 2³*⁹*⁰ = 4⁹*³*⁰ which makes perfect sense (or perhaps i missed something important)