Question

How do you write `log_4 (1/16) = -2` into its exponential form?

Answer 1

You use the definition of logarithm:
`log_ax=b => a^b=x`

So you can write your expression. taking the base `a` of the log (in this case is `4`) to the power of `b=-2` which is indeed equal to the argument of the log, i.e.:

`4^(-2)=1/4^2=1/16`

In which you use the fact that: `x^-a=1/x^a`

Alternatively you can take all as exponents of `4`:
`4^(log_4(1/16))=4^(-2)`
Which is again:
`1/16=1/16`