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WAEC Mathematics 2015 Paper

Question : 4

Total: 45

\frac{27^x \times 3^{1-x}}{9^{2x}} = 1

, find the value of x.

Solution:

Concept:

Express all powers using the same base, then compare the exponents.

Explanation:

Given equation:

\frac{27^x \times 3^{1-x}}{9^{2x}} = 1

Rewrite

27 = 3^3

and

9 = 3^2

\frac{(3^3)^x \times 3^{1-x}}{(3^2)^{2x}} = \frac{3^{3x} \times 3^{1-x}}{3^{4x}} = 1

Apply the laws of exponents:

3^{3x + 1 - x - 4x} = 3^0

Simplify the exponent:

3^{1 - 2x} = 3^0

Since the bases are equal, equate the exponents:

1 - 2x = 0

Solve for

x

2x = 1

x = \frac{1}{2}

Answer:

x = \frac{1}{2}

\;

(Option B)

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