How do you expand the following logarithm: $$ \log_5 \left(\frac{u}{v^3}\right)^6 $$
The result I got was: $$ 6\log_5u -18\log_5v $$
Is that fully expanded?
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It is correct!!!
$$\log_5 \left ( \frac{u}{v^3}\right )^6=6 \cdot \log_5 \left (\frac{u}{v^3} \right) \\= 6 \cdot (\log_5(u)- \log_5(v^3))=6 \cdot (\log_5 u-3 \log_5 v)=6\log_5 u-18 \log_5 v $$
evinda
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Do you mean $\log_5 ((\frac{u}{v^3})^6)$ or $(\log_5 (\frac{u}{v^3}))^6$? If it is the former your answer is correct; if it is the latter it simplifies to $(\log_5 (u)-3\log_5(v))^6$ instead.
Pauly B
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