SOLUTION: Condense the expression: 1/3 log(base5)8 - 1/2 log(base5)x + 4 log (base5)y Please help me solve this. Thank You for your time.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Condense the expression: 1/3 log(base5)8 - 1/2 log(base5)x + 4 log (base5)y Please help me solve this. Thank You for your time.      Log On


   

Question 29308: Condense the expression:
1/3 log(base5)8 - 1/2 log(base5)x + 4 log (base5)y
Please help me solve this. Thank You for your time.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Condense the expression:
1/3 log(base5)8 - 1/2 log(base5)x + 4 log (base5)y
since all logs are to same base 5 let us omit it for convenience.
USE THE FORMULAE
LOG(XY)=LOG(X)+LOG(Y)......LOG(X/Y)=LOG(X)-LOG(Y)....LOG(X^N)=N*LOG(X)...
1/3 log(base5)8 - 1/2 log(base5)x + 4 log (base5)y
=LOG(8)^(1/3)-LOG(X)^(1/2)+LOG(Y)^4
=LOG{2*Y^4/X^0.5)}...SINCE..8^(1/3)=2...(2^3=8)
=LOG (BASE5){2*Y^4/X^0.5)}...