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Logarithms

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Question : 21 of 85

Marks: +1, -0

Value of

16^{\log_{4}5}

is

5
25
125
$\frac{5}{64}$ .

Solution:

Concept:

Use the identity

a^{\log_a b} = b

after rewriting the base

16

as a power of

4

.

Explanation:

Rewrite

16

as

4^2

.

Then

16^{\log_4 5} = (4^2)^{\log_4 5} = 4^{2 \log_4 5}

.

Apply the power rule of logarithms:

2 \log_4 5 = \log_4 (5^2) = \log_4 25

.

Thus the expression becomes

4^{\log_4 25}

.

Using the identity

a^{\log_a b} = b

, we get

4^{\log_4 25} = 25

.

Answer:

25

(Option B).

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