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WAEC Further Mathematics 2019 Paper

Question : 1

Total: 39

Solve: 8

^{x - 2}

^{3x}

Solution:

Concept:

Express both sides of the exponential equation with the same base, then equate the exponents.

Explanation:

Given:

8^{x-2} = 4^{3x}

Write

8

and

4

as powers of

2

8 = 2^3

and

4 = 2^2

Therefore:

8^{x-2} = (2^3)^{x-2} = 2^{3(x-2)} = 2^{3x-6}

4^{3x} = (2^2)^{3x} = 2^{6x}

Now the equation becomes:

2^{3x-6} = 2^{6x}

Since the bases are equal, equate the exponents:

3x - 6 = 6x

Subtract

3x

from both sides:

-6 = 3x

Divide both sides by

3

x = -2

Answer:

x = -2

Correct option: A.

-2

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