Question

It is given that log10 2= 0.301 and log10 3 = 0.477. How many digits are there in (108)10?

A) 19 B) 20 C) 21 D) 22

Answer 1

Given :  log 2 = 0.301  and log 3  = 0.477

To Find : How many digits are there in 108¹⁰

A) 19 B) 20 C) 21 D) 22

Solution:

N = 108¹⁰

Taking log both sides

=> log N = log ( 108¹⁰)

=> log N = 10 log 108

108 = 2 x 2 x 3 x 3 x 3   =  2² * 3³

=>  log N = 10 log ( 2² * 3³)

=>  log N = 10 ( log 2² + log 3³)

=>   log N = 10 (2 log 2  + 3 log 3 )

=>  log N = 10 (2(0.301)  + 3 (0.477 ) )

=> log N = 10 ( 0.602 + 1.431)

=> log N = 10 ( 2.033)

=> log N = 20.33

Taking antilog both sides

=> N = anti log ( 20 .33)  = $10^{20.33}$

Characteristics part = 20

number of digits = 20 + 1 = 21

Number of Digits = 21

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Answer 2

Given : log 2 = 0.301 and log 3 = 0.477

To Find : How many digits are there in 108¹⁰

A) 19 B) 20 C) 21 D) 22

Solution:

N = 108¹⁰

Taking log both sides

=> log N = log ( 108¹⁰)

=> log N = 10 log 108

108 = 2 x 2 x 3 x 3 x 3 = 2² * 3³

=> log N = 10 log ( 2² * 3³)

=> log N = 10 ( log 2² + log 3³)

=> log N = 10 (2 log 2 + 3 log 3 )

=> log N = 10 (2(0.301) + 3 (0.477 ) )

=> log N = 10 ( 0.602 + 1.431)

=> log N = 10 ( 2.033)

=> log N = 20.33

Taking antilog both sides

=> N = anti log ( 20 .33) = 10^{20.33}10

20.33

Characteristics part = 20

number of digits = 20 + 1 = 21

Number of Digits = 21