Solution for Problem 4.5.1

Write in terms of the logarithms  of x, y, and z.
We want to write the expression such that the variables are as isolated as possible.

Solve

            Step

Start with division
division turns into subtraction

     =  log x + log 3 - (log 2 + log y)

 Take care of multiplication next
multiplication turns into addition
     =  log x + log 3 - log 2 - log y Distribute the minus sign 

 

 All variables are isolated


* Assume all values for x, y, and z are defined for each expression. Example log (-2) is undefined.

Property

log b MN = log b M + log b N