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  4. Number of digits in 416 ⋅ 525 is equal to (Given log 10 2=0.3010 )

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Q. Number of digits in $4^{16} \cdot 5^{25}$ is equal to (Given $\log _{10} 2=0.3010$ )

Continuity and Differentiability

Solution:

Let $N =2^{32} \cdot 5^{25}=2^7(2 \cdot 5)^{25}=128 \cdot 10^{25} $
$\Rightarrow \log _{10} N =25+7 \log _{10^2} 2=25+7 \times 0.3010=25+2.107=27.107$
$\Rightarrow N \text { is a } 28 \text { digit number. }$