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WAEC Further Mathematics 2015 Paper

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Question : 4

Total: 40

If

\log_{3} x = \log_{9} 3

, find the value of x.

$3^{2}$
$3^{\;\frac{1}{2}}$
$3^{\;\frac{1}{3}}$
$2^{13}$

Solution:

Concept:

Use the change of base or express

3

as a power of

9

.

Explanation:

Since

9 = 3^2

, we can write

3 = 9^{\frac{1}{2}}

.

So,

\log_{9} 3 = \log_{9} 9^{\frac{1}{2}} = \frac{1}{2}\log_{9} 9

.

We know

\log_{9} 9 = 1

, hence

\log_{9} 3 = \frac{1}{2}

.

Thus,

\log_{3} x = \frac{1}{2}

.

Converting to exponential form gives

x = 3^{\frac{1}{2}}

.

Answer:

x = 3^{\frac{1}{2}}

, which is option B.

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