Test Index

WAEC Further Mathematics 2010 Paper

© africaexams.com

Question : 5

Total: 40

Simplify

\;\frac{\log_{5} 8}{\log_{5} \sqrt{8}}

.

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

Solution:

Concept:

Use the power rule of logarithms:

\log_b a^n = n\log_b a

.

Explanation:

Start with the given expression:

\frac{\log_{5} 8}{\log_{5} \sqrt{8}}

Express

\sqrt{8}

as a power of

8

:

\sqrt{8} = 8^{\frac{1}{2}}

Apply the power rule to the denominator:

\log_{5} 8^{\frac{1}{2}} = \frac{1}{2}\log_{5} 8

Substitute this back into the original fraction:

\frac{\log_{5} 8}{\frac{1}{2}\log_{5} 8}

Cancel the common term

\log_{5} 8

:

\frac{1}{\frac{1}{2}} = 2

Answer:

D.

2

© africaexams.com

Go to Question:

Prev Question

Next Question