What is the number of digits in 333 ? Given that log3 = 0.47712? 12 13 14 15 Let

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Question
What is the number of digits in 333 ? Given that log3 = 0.47712?
Options
A. 12
B. 13
C. 14
D. 15

Correct Answer

13

Explanation

Let $L e t x = (3^{3^{3}})$ = ${(3^{3})}^{3}$

Then, $\log (x) = 3^{3} \log (3)$

= 27 x 0.47712 = 12.88224

Since the characteristic in the resultant value of log x is 12

$?$ The number of digits in x is (12 + 1) = 13

Hence the required number of digits in $3^{3^{3}}$ is 13.

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