Question

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

Answer 1

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

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