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

Algebra ->  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

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 Click here to see ALL problems on logarithm 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)   (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