Question

Find number of digits in 4power 2013 .if log 10power2=0.3010

Answer 1

The integer part of the log base 10 of a number equals the number of decimal digits minus 1. So x=log42013=log24026=4026×0.3010±5E−5.x=log⁡42013=log⁡24026=4026×0.3010±5E−5. This gives1211.62<x<1212.028.1211.62<x<1212.028. The given value of log102log10⁡2 is not sufficiently accurate to decide the issue, we need another decimal. log102=0.30103±5E−6.log10⁡2=0.30103±5E−6. Now we are cooking. 1211.92<x<1211.97.1211.92<x<1211.97. So the number of digits in 4201342013 is 1212.1212.

It is very well possible that the editor of this question just wanted you to plug in the given value of log2,log⁡2, but as you can see this is a sloppy way of formulating the question.