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WAEC Mathematics 2011 Paper

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Question : 34

Total: 47

If 27^x = 9^y. Find the value of

\; \frac{x}{y}

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

Solution:

Concept:

Express both sides of the exponential equation with the same base and equate the exponents.

Explanation:

Given:

27^x = 9^y

.

Write

27

and

9

as powers of

3

.

27 = 3^3

and

9 = 3^2

.

Substitute:

(3^3)^x = (3^2)^y

.

Using the power rule:

3^{3x} = 3^{2y}

.

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

So,

3x = 2y

.

Divide both sides by

y

:

3\frac{x}{y} = 2

.

Divide both sides by

3

:

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

.

Answer:

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

, which is option B.

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