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Logarithms

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Question : 36 of 85

Marks: +1, -0

The value of

\log_{2}[\log_{2}\{\log_{3}(\log_{3}(27^{3})\}]

1
0
2
3

Solution:

Concept:

Evaluate nested logarithms from the innermost outward using properties of exponents and logs.

Explanation:

First, compute

27^{3}

:

27 = 3^{3}

, so

27^{3} = (3^{3})^{3} = 3^{9}

.

Then

\log_{3}(27^{3}) = \log_{3}(3^{9}) = 9

.

Next,

\log_{3}(9) = \log_{3}(3^{2}) = 2

.

Now,

\log_{2}\{2\} = 1

.

Finally,

\log_{2}[1] = 0

.

Answer:

0

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