Question

Given log3 =0.4771. find the number of digits in 3^62
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Answer 1

Number of Digits in 3⁶² = 30

Given:

log3 =0.4771

To Find:

Number of Digits in 3⁶²

Solution:

Let say N = 3⁶²

taking log both side

log N = log 3⁶²

Using log aⁿ = n log a

log N = 62 log 3

Using log3 =0.4771

log N = 62 (0.4771)

log N = 29.5802

Taking antilog

N =  $10^{29.5802}$

Characteristics part = 29

number of digits = 29 + 1 = 30

Number of Digits in 3⁶² = 30

Answer 2

Given:

log3 =0.4771

number given = $3^{62}$

To Find:

Find the number of digits in $3^{62}$

Solution:

Let the number be x

so x = $3^{62}$

taking log on both sides of the equation

log x = log $3^{62}$

by the formulae of $loga^n=nlog a$ , we will open $log 3^{62} = 62log 3$

log x = 62log 3

put the value of log 3 in the equation

log x = 62 x 0.4771

        = 29.5802

x = $10^{29.5802}$

characteristics part = 29

therefore number of digits = 29+1=30

Hence the number of digits are 30.