Power raised to a logarithm question

[Coco12]

Homework Statement

Solve for x
7^log(base: 7) 3 = x

Homework Equations

The Attempt at a Solution

Ans is 3
Can someone explain to me how to solve for powers raised to a log like this one?

 

[jedishrfu]

y = 10 ^ x then log y = x right ?

looking at log y = x then 10 ^ log y = 10 ^ x

but 10 ^ x is y so

10 ^ log y = y

now since 10 is the base follow the same logic with base 7

 

[Kishlay]

in which grade are you??

 

[D H]

Can someone explain to me how to solve for powers raised to a log like this one?

7^x is a function: for every real number x, 7^x has a single, well-defined value. Denote this function as f(x): f(x)=7^x. Rhetorical question: What's the inverse of this function? The answer is log base 7. Denote this as f^-1(x)=log₇x.

A non-rhetorical question: Given *any* function f(x) and its inverse f^-1(x), what is f(f^-1(x)) ?