SOLUTION: which among log (base 13)169 and log (base 23)521 is greater ?(with out using calculator) thanks

Question 622632: which among log (base 13)169 and log (base 23)521 is greater ?(with out using calculator)
thanks

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
which among log (base 13)169 and log (base 23)521 is greater
Using exponential form of logs:
Base raised to log of number=number
for first case
13^x=169
x=2 which is the log of 169 base 13
..
for 2nd case
23^x=521
x=<2 which is the log of 529 base 23 (if x=2, the number=23^2=529, so x<2)
The log of the first case>log of 2nd case

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