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WAEC Further Mathematics 2014 Paper

Question : 1

Total: 40

\;\frac{1}{5^{-y}} = 25(5^{4-2y})

, find the value of y.

Solution:

Concept:

Use laws of exponents to write both sides with the same base, then equate the powers.

Explanation:

Start with the given equation:

\frac{1}{5^{-y}} = 25(5^{4-2y})

Since

\frac{1}{5^{-y}} = 5^y

, rewrite the LHS:

5^y = 25(5^{4-2y})

Express

25

5^2

5^y = 5^2(5^{4-2y})

Add the exponents on the RHS:

5^y = 5^{2+4-2y} = 5^{6-2y}

The bases are equal, so equate the exponents:

y = 6 - 2y

3y = 6

y = 2

Answer:

y = 2

Correct option: B.

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