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Logarithms Practice Test 2

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Question : 5 of 39

Marks: +1, -0

Find the value of

\frac{\log \sqrt{8}}{\log 8} .

$\frac{1}{2}$
$\frac{1}{4}$
$\frac{1}{2 \sqrt{2}}$
$\frac{1}{8}$

Solution:

Concept:

Use the logarithmic power rule:

\log a^n = n\log a

.

Explanation:

Given expression:

\frac{\log \sqrt{8}}{\log 8}

.

Write

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

.

So,

\log\sqrt{8}=\log(8^{1/2})

.

By the power rule,

\log(8^{1/2})=\frac{1}{2}\log 8

.

Substitute this:

\frac{\frac{1}{2}\log 8}{\log 8}

.

Cancel

\log 8

from numerator and denominator.

This gives

\frac{1}{2}

.

Answer:

\frac{1}{2}

(Option A).

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