# Question on Logarithm

• July 19th 2007, 02:15 AM
acc100jt
Question on Logarithm
If [I]x[I] is a n-digit whole number, write down the range of values of
lgx. There are 168 digits in 47^100. How many digits are there in
47^47?
Extend the result in an appropriate manner.

I got the answer, which is 79 digits.
But I'm not sure how to extent the result. How to extend? Anyone can help?
• July 19th 2007, 03:40 AM
CaptainBlack
[quote=acc100jt;61258]If x is a n-digit whole number, write down the range of values of
lgx.
[quote]

defined this way $10^{n-1}, so assuming that
$\lg$ denotes log to the base 10, we have:

$
n-1< \log_{10}(n) < n
$

RonL