Question

What is the relationship between `y=3^x` and `y=log_3x`?

Answer 1

They are inverse functions. We use the following proof to show that particular function is another's inverse.

If `f(x)` and `f^-1(x)` are inverse functions, then `f(f^-1(x)) = x`.

Let `f(x) = log_3(x)` and `f^-1(x) = 3^x`

`f(f^-1(x)) = log_3(3^x) = xlog_3(3) =(xlog3)/log3 = x`

This proves that the relationship between the two functions is that they're inverses.

Hopefully this helps!