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Logarithms Practice Test 2

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Question : 14 of 39

Marks: +1, -0

If

\log 2 = 0.3010

, then find number of digits in

2^{1070}

.

322
320
323
230
321

Solution:

Concept:

Number of digits of

N

is

1

more than the characteristic of

\log_{10} N

.

Explanation:

Let

x = 2^{1070}

.

Take

\log_{10}

on both sides:

\log_{10} x = \log_{10}(2^{1070})

.

Using the power rule,

\log_{10} x = 1070 \log_{10} 2

.

Substitute

\log_{10} 2 = 0.3010

:

\log_{10} x = 1070 \times 0.3010 = 322.07

.

The characteristic is

322

.

Thus, number of digits

= 322 + 1 = 323

.

Answer:

The number of digits in

2^{1070}

is

323

.

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