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

How would you write the following expression as a sum or difference?-example-1
User Jim Aho
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1 Answer

4 votes

Answer:

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.

User Vipul Purohit
by
7.1k points
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