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:

`16^(-1"/"2)=1/(16^(1"/"2))=1/sqrt16=1/4`

And as a logarithm, this can be written as:

`log_16(1/4) = −1/2`

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