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JAMB Mathematics 2015 Paper

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Question : 7

Total: 61

Simplify log₁₀1.5 + 3 log₁₀2 − log₁₀0.3

log₁₀4
log₁₀40
log₁₀-40
log₁₀4^-

Solution:

Concept:

Use the laws of logarithms to combine terms into a single logarithm.

Explanation:

The power rule gives

3\log_{10}2 = \log_{10}(2^3) = \log_{10}8

.

So the expression becomes

\log_{10}1.5 + \log_{10}8 - \log_{10}0.3

.

Using

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

and

\log a - \log b = \log\left(\frac{a}{b}\right)

:

\log_{10}1.5 + \log_{10}8 - \log_{10}0.3 = \log_{10}\left(\frac{1.5 \times 8}{0.3}\right)

.

Now

\frac{1.5 \times 8}{0.3} = \frac{12}{0.3} = 40

.

Therefore, the simplified form is

\log_{10}40

.

Answer:

\log_{10}40

Correct option: B.

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