If \(log_{y}\frac{1}{8}\) = 3, find the value of y.

Assessment: WAEC SSCE - Further Mathematics - 2017 (Objective) Subject: Further Mathematics

Question 1 Report

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 \(\frac{1}{2}\).
Read lesson note on Indices And Logarithmic Functions (WAEC)
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