Expert: Paul Klarreich - 5/9/2007

Question
Find a rational number which is 50 times its log to the base 10

Answer
Questioner:   sumati
Category:  Advanced Math
Private:  No
 
Subject:  LOG question
Question:  Find a rational number which is 50 times its log to the base 10
............................................
Hi, Sumati,

Your equation is:   n = 50 log n

Assuming  n = 10^x, you want to have:

10^x = 50x

x = 2  satisfies this nicely.  So  n = 100 should be your answer.

log 100 = 2,  100 = 50 * 2

It seems to me that for x = any integer that is a power of 2, you will have an example of this.  Such as:

x = 2^2 = 4 = log n,  n = 10^4 = 10000

10000 = 2500 log 10000
...................

x = 2^3 = 8 = log n,  n = 10^8 = 100000000

100000000 = 12500000 log 100000000