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JAMB Mathematics 2024 Paper

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Question : 5

Total: 50

Solve 16

^{x}

= 0.25

- $\; \frac{1}{2}$
$\; \frac{1}{4}$
- $\; \frac{1}{4}$
$\; \frac{1}{2}$

Solution:

Concept:

Rewrite both sides of the equation using the same base, then compare the exponents.

Explanation:

Start with

16^x = 0.25

.

Convert

0.25

to a fraction:

0.25 = \frac{25}{100} = \frac{1}{4}

Since

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

, the equation becomes:

16^x = 4^{-1}

Rewrite

16

as

4^2

:

(4^2)^x = 4^{-1}

This simplifies to:

4^{2x} = 4^{-1}

The bases are equal, so equate the exponents:

2x = -1

Divide both sides by

2

:

x = -\frac{1}{2}

Answer:

x = -\frac{1}{2}

, which is option A.

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