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

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Solution

The correct option is C 9
$y = 3^{12} \times 2^{8} \Rightarrow l o g_{10} y = 12 l o g_{10} 3 + 8 l o g_{10} 2$
$= 12 \times 0.47712 + 8 \times 0.30103$
= 5.72544 + 2.40824 = 8.13368
$∴$ Number of digits in y = 8 + 1 = 9

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