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JAMB Mathematics 2024 Paper

Question : 25

Total: 50

Find x if

\frac{16^{2+x}}{4} = 64^x

Solution:

Concept:

Rewrite every term as a power of the same base, then compare the exponents.

Explanation:

Use

16=2^4

4=2^2

, and

64=2^6

The equation becomes

\frac{(2^4)^{2+x}}{2^2}=(2^6)^x

Simplify using index laws:

\frac{2^{4(2+x)}}{2^2}=2^{8+4x-2}=2^{6+4x}

The right side simplifies to

2^{6x}

Since the bases are the same, equate the exponents:

6+4x=6x

Subtract

4x

from both sides:

6=2x

Divide both sides by

2

x=3

Answer:

x=3

, so the correct option is A.

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