LogarithmicProperties

Question

1. Condense the following expressions into a single logarithm by applying the properties of logarithms.You are only allowed to use integer exponents.
2. Use sqrt(...) to deal with fractional exponents.
3. Make sure your final answer is written as a single logarithm.

9/2log(x)-3/2log(y)-9/2log(z)=

Answer 1

First, move the exponents into the logs.

3(log(x^3/2) - log(y^1/2)-log(z^3/2))

Subtract means division

3(log(x^3/2/(y^1/2z^3/2)) = 3 log(√(x³/(yz³)) = log( ( sqrt(x³/(yz³)) )³ )