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WAEC Further Mathematics 2015 Paper

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Question : 3

Total: 40

Solve:

4(2^{x^2}) = 8^{x}

(1, 2)
(1, -2)
(-1, 2)
(-1, -2)

Solution:

Concept:

Rewrite both sides as powers of the same base

2

, then compare the exponents.

Explanation:

Start with

4(2^{x^2}) = 8^x

.

Write

4

as

2^2

and

8

as

2^3

.

So,

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

.

Using exponent laws,

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

.

Since the bases are equal, equate the exponents:

2 + x^2 = 3x

.

Rearrange:

x^2 - 3x + 2 = 0

.

Factorise:

(x - 1)(x - 2) = 0

.

Therefore,

x = 1

or

x = 2

.

Answer:

x = 1, 2

, which gives option A:

(1, 2)

.

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