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Guys I need some help with this problem I get the basic concept but I am having trouble with this one question if you can give me a hand.

Write the expression $\log\left(\dfrac{1000}{a^4 \sqrt{b}}\right)$ in terms of $\log a$ and $\log b$.

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  • $\begingroup$ We encourage users to accept answers that are helpful. To accept an answer, simply click on the $\checkmark$ to the left of the answer you'd like to accept. (You can accept only one answer per question.) $\endgroup$ – amWhy Apr 18 '13 at 20:39
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$$ \begin{align*} \log\left(\frac{1000}{a^4 \sqrt{b}}\right) &= \log(1000) - \log(a^4 \sqrt{b}) \quad (\mbox{quotient rule})\\ &= 3 - (\log(a^4) + \log(b^{1/2})) \quad (\mbox{product rule, $\log(1000) = 3$, $\sqrt{b} = b^{1/2}$})\\ &= 3 - 4\log(a) - \frac{1}{2} \log b \qquad (\mbox{distribute negative, power rule}) \end{align*} $$

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