Expanding Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as the sum, difference, or multiple of logarithms.

In (1 - x/3x) ^3

3 ln (1-x) - 3 ln3 - 3 ln x

Step-by-step explanation:

We have the following logarithmic expression.

ln (1-x/3x) ³

We apply the logarithm power rule.

3 ln (1-x/3x)

We apply the logarithm quotient rule.

3. [ln (1-x) - ln 3x]

We apply the logarithm product rule.

3. [ln (1-x) - (ln3 + ln x) ]

3. [ln (1-x) - ln3 - ln x]

We apply the distributive property.

3 ln (1-x) - 3 ln3 - 3 ln x