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WAEC Mathematics 2010 Paper

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Question : 13

Total: 49

Given that

\frac{5^{n+3}}{25^{2n-3}}

= 5º, find n

n = 1
n = 2
n = 3
n = 5

Solution:

Concept:

Use the laws of indices by writing

25

as

5^2

and then equate the powers.

Explanation:

Given equation:

\frac{5^{n+3}}{25^{2n-3}} = 5^0

Since

25 = 5^2

, rewrite the denominator:

\frac{5^{n+3}}{(5^2)^{2n-3}} = \frac{5^{n+3}}{5^{4n-6}}

Using

\frac{a^m}{a^n} = a^{m-n}

, we get:

5^{(n+3)-(4n-6)} = 5^0

Equating the exponents:

n+3-4n+6 = 0

-3n+9 = 0

-3n = -9

n = 3

Answer:

n = 3

, so the correct option is C.

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