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Logarithms Practice Test 1

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Question : 20 of 40

Marks: +1, -0

If

\log_3 x + 2\log_9 x + 3\log_{27} x = 12

then x is:

81
36
64
None of these
Undefined

Solution: 👈: Video Solution

Concept:

Use change of base to write every logarithm in base

3

.

Explanation:

Given:

\log_3 x + 2\log_9 x + 3\log_{27} x = 12

.

Convert:

\log_9 x = \frac{\log_3 x}{\log_3 9} = \frac{\log_3 x}{2}

.

So

2\log_9 x = \log_3 x

.

Also

\log_{27} x = \frac{\log_3 x}{\log_3 27} = \frac{\log_3 x}{3}

.

So

3\log_{27} x = \log_3 x

.

Substitute:

\log_3 x + \log_3 x + \log_3 x = 12

.

Thus

3\log_3 x = 12

.

So

\log_3 x = 4

.

Therefore

x = 3^4 = 81

.

Answer:

x = 81

, so option A is correct.

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