Question

How would you write the following expression as a sum or difference?

Answer 1

B

Explanation:

Look at the expression inside the log( ). Work from the outside in, so to speak. First, there's a quotient (the cube root divided by 3x).

`\log \left( \frac{\sqrt[3]{2-x}}{3x} \right) = \log\left(\sqrt[3]{2-x}}\right) - \log{3x}`

The cube root can be written using a rational exponent.

`\log\left(\sqrt[3]{2-x}}\right) - \log{3x} = \log \left( (2-x)^(1/3) \right) - \log{3x}`

Use the exponent property to move the exponent 1/3 out.

`\log (2-x)^(1/3) - \log{3x} = (1)/(3) \log{(2-x)} - \log{3x}`

This now matches answer choice B.