If \(log_{y}\frac{1}{8}\) = 3, find the value of y.
Answer Details
We can use the definition of logarithms to solve for y.
Recall that logarithms are the inverse function of exponential functions. That is, if we have:
y = b^x
Then the logarithm base b of y is:
log_b y = x
Using this definition, we can write:
log_y (1/8) = 3
As an exponential function:
y^3 = 1/8
Simplifying the right side:
y^3 = (1/2)^3
Taking the cube root of both sides:
y = 1/2
Therefore, the answer is \(\frac{1}{2}\).