SOLUTION: Simplify the following expression. Your answer should not contain logarithms. 25^log5(x) (that's log base 5 then x)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Simplify the following expression. Your answer should not contain logarithms. 25^log5(x) (that's log base 5 then x)      Log On


   

Question 22276: Simplify the following expression. Your answer should not contain logarithms.

25^log5(x)
(that's log base 5 then x)
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
LET Y=25^(LOG X TO BASE 5)
USE FORMULA LOG X TO BASE 5 = LOG X/LOG 5 TO COMMON BASE
Y=25^(LOG X/LOG 5)
TAKING LOGS BOTH SIDES
LOG Y ={(LOG X)/(LOG 5)}*LOG 25
=LOG X*LOG 5^2/LOG 5=LOG X*(2*LOG 5)/LOG 5(SINCE LOG X^N=N*LOG X)
=2LOG X=LOG X^2
HENCE LOG Y = LOG X^2
TAKING ANTILOGS
Y=X^2
HENCE
Y=25^(LOG X TO BASE 5)=X^2