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Logarithms

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Question : 3 of 85

Marks: +1, -0

The number of digits in

3^{12}

\log 3 = 0.4771

)

5
6
12
11

Solution:

Concept:

The number of digits in a positive integer

N

is given by

\lfloor \log_{10} N \rfloor + 1

.

Explanation:

We need the number of digits in

3^{12}

.

Compute

\log_{10}(3^{12}) = 12 \times \log_{10} 3

.

Given

\log_{10} 3 = 0.4771

, so

12 \times 0.4771 = 5.7252

.

The floor (integer part) is

5

.

Number of digits =

5 + 1 = 6

.

Answer:

B. 6

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