Question

How do you evaluate `log_15(15)`?

Answer 1

`log_a(a) = 1` holds for any positive integer `a`.

Explanation:

You are basically searching for `x` so that

`log_(15)(15) = x`

The inverse function of the `log_15(z)` is `15^z`which means that
`log_15(15^z) = z` and also `15^(log_15(z)) = z` always hold.

This means that to "get rid" of the logarithmic term, you can perform `15^z` on both sides of your equation:

`color(white)(xxx)15^(log_15(15)) = 15^x`

`<=> color(white)(xxxxx) 15 = 15^x`

`<=> color(white)(xxxxx) 15^1 = 15^x`

So you can see that `x = 1` which means that

`log_15(15) = 1`