−6 ln x − 7 ln y + 1/7 ln z

Question

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression as the logarithm of one quantity.
−6 ln x − 7 ln y + 1/7 ln z

Answer 1

A logarithm of one quantity means a logarithm with a single argument, or single logarithm term.

 

The coefficient of logs is the exponent of the log's base.

 

ln(x^-6) + ln(y^-7) + ln(z^1/7)

 

 

When we add logs, we are multiplying the arguments.

 

ln(x^-6y^-7z^1/7)

 

 

Since the variables have to be positive,

 

ln(⁷√z / (x⁶y⁷))

 

 

Note that the numerator is the 7th-root of z.