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Logarithms

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Question : 2 of 85

Marks: +1, -0

The base in logarithm of

\log_{a} 32 = \frac{10}{3}

a

is equal to

4
$\sqrt{8}$
2
$\frac{2}{3}$

Solution:

Concept:

Logarithm

\log_a 32 = \frac{10}{3}

means

a^{10/3} = 32

.

Explanation:

Given:

\log_a 32 = \frac{10}{3}

.

Rewrite in exponential form:

a^{10/3} = 32

.

Since

32 = 2^5

, we have

a^{10/3} = 2^5

.

Raise both sides to the power

\frac{3}{10}

:

(a^{10/3})^{3/10} = (2^5)^{3/10}

.

This simplifies to

a = 2^{5 \cdot \frac{3}{10}} = 2^{15/10} = 2^{3/2}

.

Now

2^{3/2} = \sqrt{2^3} = \sqrt{8}

.

Thus

a = \sqrt{8}

.

Answer:

B.

\sqrt{8}

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