History, asked by raghusrinadhgmailcom, 3 months ago

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

Answers

Answered by SharadSangha
0

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.

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