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Logarithms Practice Test 1

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Question : 5 of 40

Marks: +1, -0

If

\log_4 7 = x

\log_7 16

is equal to:

$\frac{2}{x}$
$x$
$2x$
$x^2$

Solution: 👈: Video Solution

Concept:

Use the reciprocal property of logarithms and the power rule.

Explanation:

Given

\log_4 7 = x

.

By reciprocal relation,

\log_7 4 = \frac{1}{x}

.

Write

16 = 4^2

.

So,

\log_7 16 = \log_7 (4^2)

.

Using the power rule,

\log_7 (4^2) = 2\log_7 4

.

Substitute

\log_7 4 = \frac{1}{x}

.

Thus,

\log_7 16 = 2 \cdot \frac{1}{x} = \frac{2}{x}

.

Answer:

\log_7 16 = \frac{2}{x}

, which is option A.

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