Given, ${log}_{10} 2 = 0.3103, {log}_{10} 3 = 0.47712$ , then find the number of digits in $3^{12} \times 2^{8}$

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Solution

Let, $x = 3^{12} \times 2^{8} .$ Then
${log}_{10} x = 12 log 3 + 8 log 2$
$= 12 \times 0.47712 + 8 \times 0.30103$
$= 5.72544 + 2.40824 = 8.13368.$
Therefore, $x = 10^{8.13368}$
Hence, the number of digits in $3^{12} \times 2^{8}$ is $8 + 1 = 9.$
Ans: 9

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