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WAEC Mathematics 2019 Paper

Question : 17

Total: 50

If (0.25)

^y

= 32, find the value of y.

Solution:

Concept:

Express both numbers as powers of the same base, then equate the exponents.

Explanation:

We start with

(0.25)^y = 32

Write

0.25

as a fraction:

0.25 = \frac{1}{4}

Since

\frac{1}{4} = 2^{-2}

, we replace

0.25

with

2^{-2}

Therefore,

(0.25)^y = (2^{-2})^y = 2^{-2y}

Next, write

32

as a power of

2

32 = 2^5

Now the equation becomes

2^{-2y} = 2^5

Because the bases are equal, the exponents must also be equal.

So we get

-2y = 5

Divide both sides by

-2

y = \frac{5}{-2} = -\frac{5}{2}

This matches option A.

Answer:

y = -\frac{5}{2}

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