Question: If $\log_{10}2 = 0.30103,\log_{10}3 = 0.47712,$ the number of digits in$3^{12} \times 2^{8}$is...

Question

If $\log_{10}2 = 0.30103,\log_{10}3 = 0.47712,$ the number of digits in $3^{12} \times 2^{8}$ is

Answer 1

$y = 3^{12} \times 2^{8}$ $\Rightarrow$ $\log_{10}y = 12\log_{10}3 + 8\log_{10}2$

$= 12 \times 0.47712 + 8 \times 0.30103$

$= 5.72544 + 2.40824 = 8.13368$

$\therefore$ Number of digits in $y$ = 8 + 1 = 9.

Question: If \(\log_{10}2 = 0.30103,\log_{10}3 = 0.47712,\) the number of digits in\(3^{12} \times 2^{8}\)is...