System of equations with logarithms (answer confirmation)

Question

${\log }_a{\left(x^{{\log }_a{\left(x^{{\log }_a{\left(x\right)}^4}\right)}^3}\right)}^2=a^{64}$ ,

$x^{a^x}=a^{2a^{x+1}}$ solve for x.

i've got this system of equations from college and supposedly the answer is x = 2 as integer, at least that's what my college book says, but i can't obtain that result.

The result i get is 2.0157...

So... is my answer wrong or is x=2 a wrong answer?

Answer 1

Hello, thank you for taking the time to post your question!

My guess is that they were reporting the value of x = 2 after rounding! Sometimes you see that happen on questions that are expecting physical quantities for the answer ... meaning that it wouldn’t make sense to have like a fraction of a part or something like that. So I'm guessing they rounded the 2.0157 to the nearest whole value of 2.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)