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Logarithms Practice Test 1

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Question : 15 of 40

Marks: +1, -0

If

\log 3 = 0.4771

, then find the number of digits in

3^{100}

.

79
48
52
117
Cannot be determined

Solution: 👈: Video Solution

Concept:

If

\log_{10} x = n

, then the number of digits in

x

is the characteristic of

n

plus

1

.

Explanation:

Let

x = 3^{100}

.

Take

\log_{10}

on both sides:

\log_{10} x = \log_{10}(3^{100})

.

Using

\log_b(a^m)=m\log_b a

:

\log_{10} x = 100\log_{10}3

.

Substitute

\log_{10}3=0.4771

:

\log_{10} x = 100 \times 0.4771 = 47.71

.

The characteristic is

47

.

Therefore, number of digits

=47+1=48

.

Answer:

3^{100}

has

48

digits.

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