SOLUTION: Assume that x,y,z and b are positive numbers. Use the properties of logarithms to write each expression in terms of the logarithms of x,y, and z. log(base b)x^(1/2) y^3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Assume that x,y,z and b are positive numbers. Use the properties of logarithms to write each expression in terms of the logarithms of x,y, and z. log(base b)x^(1/2) y^3      Log On


   

Question 315427: Assume that x,y,z and b are positive numbers. Use the properties of logarithms to write each expression in terms of the logarithms of x,y, and z.
log(base b)x^(1/2) y^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We're going to use the following identities:

1) log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29

2) log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29



So first using identity #2 and then identity #1, we get:





So in short,