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WAEC Further Mathematics 2018 Paper

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Question : 12

Total: 40

Solve

\log_{2}(12x - 10) = 1 + \log_{2}(4x + 3)

.

4.75
4.00
1.75
1.00

Solution:

Concept:

Convert the constant

1

into a logarithm base

2

, then combine the logarithmic terms.

Explanation:

Write

1

as

\log_{2}2

.

So the equation becomes

\log_{2}(12x - 10) = \log_{2}2 + \log_{2}(4x + 3)

.

Using

\log a + \log b = \log(ab)

, we get

\log_{2}(12x - 10) = \log_{2}\bigl(2(4x + 3)\bigr)

.

Since the bases are equal, equate the arguments:

12x - 10 = 2(4x + 3)

12x - 10 = 8x + 6

12x - 8x = 6 + 10

4x = 16

x = 4

.

Answer:

x = 4

This corresponds to option B.

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