Question

solve this logarithm question​

Answer 1

Answer:

48

Step-by-step explanation:

$log( {3}^{2} ) = 2 \times log(3) = 2 \times 0.4771 = 0.9542$

$log( {3}^{2} ) = 0.9542 = \: 1 \: (approx)$

${3}^{2} = 9 ( Number\:of \:digits\: 1)$

Similarly

$log( {3}^{4} ) = 1.9084 = 2 (approx)$

${3}^{4} = 81 ( Number\:of\: digits\: 2)$

$log( {3}^{6} ) = 2.8626 = 3 (approx)$

${3}^{6} = 729 ( Number\:of \:digits \:3)$

$log( {3}^{100} ) = 100 log(3) = 100 \times 0.4771 = 47.71 = 48 (approx)$

Number of digits in ${3}^{100} = 48$