Test Index

WAEC Further Mathematics 2012 Paper

© africaexams.com

Question : 6

Total: 40

Evaluate

\log_{10}\left(\;\frac{1}{3} + \;\frac{1}{4}\right) + 2\log_{10} 2 + \log_{10}\left(\;\frac{3}{7}\right)

-3
0
$\;\frac{5}{6}$
1

Solution:

Concept:

Use logarithm laws:

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

and

n\log a = \log(a^n)

.

Explanation:

First simplify the fraction inside the first logarithm:

\frac{1}{3} + \frac{1}{4} = \frac{7}{12}

.

Rewrite

2\log_{10} 2

as

\log_{10} 2^2 = \log_{10} 4

.

Now combine all three logarithms into one:

\log_{10}\left(\frac{7}{12}\right) + \log_{10} 4 + \log_{10}\left(\frac{3}{7}\right) = \log_{10}\left(\frac{7}{12} \times 4 \times \frac{3}{7}\right).

Simplify inside the logarithm:

\frac{7}{12} \times 4 \times \frac{3}{7} = \frac{7 \times 4 \times 3}{12 \times 7} = 1.

So the expression becomes

\log_{10} 1 = 0

.

Answer:

Option B:

0

© africaexams.com

Go to Question:

Prev Question

Next Question