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WAEC Mathematics 2013 Paper

Question : 20

Total: 48

If 2 log x (3

\;\frac{3}{8}

) = 6, find the value of x

Solution:

Concept:

A logarithmic equation can be rewritten as an exponential equation to find the unknown base.

Explanation:

Given:

2\log_x\left(3\frac{3}{8}\right)=6

Divide both sides by

2

\log_x\left(3\frac{3}{8}\right)=3

Convert the mixed fraction:

3\frac{3}{8}=\frac{27}{8}

So,

\log_x\left(\frac{27}{8}\right)=3

Using the definition of logarithms:

x^3=\frac{27}{8}

Take the cube root of both sides:

x=\sqrt[3]{\frac{27}{8}}=\frac{\sqrt[3]{27}}{\sqrt[3]{8}}

x=\frac{3}{2}

Answer:

x=\frac{3}{2}

, which is Option A.

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