Question

if log10 3=0.4771, then the number of digits in (81)power21 is​

Answer 1

Given,

$log_{10}3$=0.4771

To find,

Number of digits in $81^{21}$

Solution,

We start with finding the log to the base 10 for the given number.

The answer will give us the number to which the power of 10 should be raised to get the given number.

The answer comes out to be A = i + d, where i is the integer part and d is the decimal part.

$log_{10} 81^{21} = log_{10} (3^{3})^{21} = log_{10} 3^{63} = 63log_{10} 3 = 63*0.4771$

Value of  $log_{10}81^{21} = 30.05$

The given number can be represented as $10^{30.05}$.

Simplifying further, we get $10^{30}*10^{0.05}$

Ten to the power 0.05 is greater than one.

Therefore, the given number will have 30 digits.