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Logarithms Practice Test 2

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Question : 7 of 39

Marks: +1, -0

If

x = \log_6 \log_7(117649)

, then find the value of

\log_5 5^{2^x}

.

0
1
2
3
Undefined

Solution:

Concept:

Use the logarithmic identities

\log_a a^m = m

and

\log_a a = 1

to simplify nested logarithms.

Explanation:

Write

117649

as a power of

7

:

7^6 = 117649

, so

\log_7(117649)=6

.

Therefore,

x=\log_6 6=1

.

Substitute

x=1

into

\log_5 5^{2^x}

:

\log_5 5^{2^1} = \log_5 5^2

.

Using

\log_a a^m = m

, this gives

2

.

Answer:

\log_5 5^{2^x}=2

, so the correct option is C.

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