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WAEC Further Mathematics 2022 Paper

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Question : 3

Total: 45

If

\log_{10}(3x-1) + \log_{10}4 = \log_{10}(9x+2)

, find the value of x

$\; \frac{1}{3}$
1
2
3

Solution:

Concept:

Use the logarithm product rule to combine terms, then equate the arguments.

Explanation:

Given

\log_{10}(3x-1) + \log_{10}4 = \log_{10}(9x+2)

.

Apply

\log_{10}a + \log_{10}b = \log_{10}(ab)

.

So,

\log_{10}[4(3x-1)] = \log_{10}(9x+2)

.

Since the bases are equal, equate the arguments.

4(3x-1) = 9x+2

.

12x - 4 = 9x + 2

.

12x - 9x = 2 + 4

.

3x = 6

.

x = 2

.

Answer:

x = 2

Correct option: C.

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