If \(log_{y}\frac{1}{8}\) = 3, find the value of y.
- -2
- -\(\frac{1}{2}\)
-
\(\frac{1}{2}\)
- 2
The correct answer is: C
Explanation
\(log_{y}\frac{1}{8} = 3 \implies y^{3} = \frac{1}{8}\) (Laws of logarithm)
\(y^{3} = \frac{1}{2^{3}} = (\frac{1}{2})^{3}\)
Equating both sides, we have
\(y = \frac{1}{2}\)