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Question

Mathematics Question on Logarithms

If log2log2 = 0.30103, find number of digits in 256

A

13

B

15

C

17

D

19

Answer

17

Explanation

Solution

The correct is option (C): given log2log2=0.30103
let x= 256
logxlogx=log256log2^{56}
log(x)log(x)=56log(2)56log(2)
log(x)log(x)= 56×0.3010356 \times 0.30103 = 16.85
The no. of digits in 256 = 17