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WAEC Further Mathematics 2011 Paper

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Question : 3

Total: 40

If

\log_{9} 3 + 2x = 1

, find x.

$-\frac{1}{2}$
$-\frac{1}{4}$
$\frac{1}{4}$
$\frac{1}{2}$

Solution:

Concept:

Recognise the value of the given logarithm and then solve the resulting linear equation for

x

.

Explanation:

Since

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

, we get

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

.

Substitute this into the given equation:

\frac{1}{2} + 2x = 1

.

Subtract

\frac{1}{2}

from both sides:

2x = 1 - \frac{1}{2} = \frac{1}{2}

.

Divide both sides by

2

:

x = \frac{1}{4}

.

Answer:

x = \frac{1}{4}

This is option C.

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