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WAEC Mathematics 2021 Paper

Question : 10

Total: 49

If 16 * 2

^{(x + 1)}

^x

^{(1 - x)}

, find the value of x.

Solution:

Concept:

Express every term as a power of the same base, then equate the exponents.

Explanation:

Rewrite

16

4^x

, and

8^{1-x}

using base

2

16 = 2^4

4^x = 2^{2x}

8^{1-x} = 2^{3(1-x)}

The equation becomes:

2^4 \cdot 2^{x+1} = 2^{2x} \cdot 2^{3(1-x)}

Add the exponents on both sides:

2^{x+5} = 2^{2x + 3 - 3x}

Simplify the exponent on the right:

2^{x+5} = 2^{3 - x}

Since the bases are equal, equate the exponents:

x + 5 = 3 - x

Collect like terms:

x + x = 3 - 5

2x = -2

Divide both sides by

2

x = -1

Answer:

x = -1

, which is option D.

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