Using the log laws, we can write this as:

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

And using the rule for negative exponents gives:

`b^(1/2)=4`

Squaring both sides gives: `b = 16`.

Checking our answer, we have:

And as a logarithm, this can be written as:

`log_16(1/4) = −1/2`