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WAEC Further Mathematics 2017 Paper

Question : 1

Total: 40

\log_{y}\;\frac{1}{8}

= 3, find the value of y.

Solution:

Concept:

Change the logarithmic equation into its equivalent exponential form using the definition of a logarithm.

Explanation:

Given

\log_{y}\frac{1}{8}=3

By definition, if

\log_{y}a=b

, then

y^{b}=a

So,

\log_{y}\frac{1}{8}=3

implies

y^{3}=\frac{1}{8}

Now write

\frac{1}{8}

as a power of

\frac{1}{2}

\frac{1}{8}=\frac{1}{2^{3}}=\left(\frac{1}{2}\right)^{3}

Thus,

y^{3}=\left(\frac{1}{2}\right)^{3}

Since the exponents are equal, the bases must also be equal.

Therefore,

y=\frac{1}{2}

Answer:

y=\frac{1}{2}

which is Option C.

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