Question

If log2 = 0.3010 and log3 = 0.4771 then the number of digits in 6^17

Answer 1

Concept:

$log(e^{x})=elogx$

Given:

$log2 = 0.3010\\log3 = 0.4771$

To find:

$log(6^{17})$

Solution:

In this question, we have applied the concept of the log, which is $log(e^{x})=elogx$

now, we know that

$log2 = 0.3010\\log3 = 0.4771$

so, by putting the formula in the question, and the values of log2 and log3, we get

$log(6^{17} )=17log6=17(log3+log2)=17*(0.4771+0.3010)\\=17*0.7781=13.2277no. of digits =13+1=14$

Hence, the total number of digits is 14.

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