Mathematical Challenge | Learn how to solve exponential equation quickly | Math Olympiad Training

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Mathematical Challenge | Learn how to solve exponential equation quickly | Math Olympiad Training

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[alster]

Easy. Got it in 5 seconds. Cheers from The Philippines 🇵🇭

[innocentonly]

Can we stop at stage where it is x²=1
X²=(-1)²
So x=1 or x= -1

[justabunga]

Well, we cannot just set the exponents equal to each other because one tends to lose one of the solutions since one of the solutions could be x=0. Here, it's a good thing that x cannot be 0 since 0^0 and 0^(1/0) are both undefined. Usually, the correct way to do that from here is to either take the log on both sides or change the base in the variable to any base. Here, if we want to extend more possible values, I have to take the absolute value on both sides and then take the log on both sides. This would take it as xln(|x|)-ln(|x|)/x=0. Factor ln(|x|) gives us (x-1/x)ln(|x|)=0 so x=±1.

[shesharajnavada]

I have a question
In above; we get
x²=1
Therefore,
x=±sqrt(1)??

[zawatsky]

0⁰ не определён и делить на 0 нельзя, потому остаётся только 1.

[michaelkouzmin]

Do you consider x^x - exponential function or power function? What is its domain?
IMHO: If it is exponential then x should be positive as its basis.

[williamwingo]

Don't see what all the fuss is about. x = 1/x; and 1 and --1 come immediately to mind. 🤠