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Logarithms

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Question : 12 of 85

Marks: +1, -0

If

\log_{2}[\log_{3}(\log_{2} x)]=1

x

is

256
512
81
128

Solution:

Concept:

Use the definition of logarithm: if

\log_a b = c

, then

a^c = b

.

Explanation:

Start from the outermost logarithm:

\log_{2}[\log_{3}(\log_{2} x)] = 1

.

Let

A = \log_{3}(\log_{2} x)

. Then

\log_{2} A = 1

.

By definition,

A = 2^1 = 2

.

So

\log_{3}(\log_{2} x) = 2

.

Again, by definition,

\log_{2} x = 3^2 = 9

.

Finally,

x = 2^9 = 512

.

Answer:

512 (Option B).

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