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Question

The value of log7(log7 7(77)) is:

A
13log72
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B
3log72
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C
73log72
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D
12log73
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Solution

The correct option is A 13log72
Let, L=log7(log7 7(77))

Let's simplify 7(77) first.

7(77)=7(7×71/2)
=7(73/2)
=7(73/2)1/2
=7×73/4
=77/4
=(77/4)1/2
=77/8

L=log7(log7 7(77))
=log7(log7 77/8)
=log7(78)
=log7 7log7 8 =1log7 23 =13log72

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