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WAEC Mathematics 2013 Paper

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Question : 2

Total: 48

If 9^{(2 - x)} = 3, find x

1
$\; \frac{3}{2}$
2
$\; \frac{5}{2}$

Solution:

Concept:

Rewrite 9 as a power of 3 and equate the exponents.

Explanation:

Given:

9^{(2-x)} = 3

Since

9 = 3^2

, we write:

(3^2)^{(2-x)} = 3

Using the power rule:

3^{2(2-x)} = 3^1

Bases are equal, so equate exponents:

2(2-x) = 1

Expand:

4 - 2x = 1

Subtract 4 from both sides:

-2x = 1 - 4

-2x = -3

Divide both sides by

-2

:

x = \frac{-3}{-2} = \frac{3}{2}

Answer:

x = \frac{3}{2}

, which is option B.

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