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If $$r$$ and $$s$$ are positive real numbers such that $$\log(rs) = 10$$ and $$\log\left(\frac{r}{s}\right) = 2$$ then $$3\log(r) + 5\log(s) =$$ ____
Correct Answer: 38
$$\log r + \log s = 10$$ and $$\log r - \log s = 2$$. Adding and subtracting gives $$\log r = 6$$ and $$\log s = 4$$. So $$3\log r + 5\log s = 18 + 20 = 38$$.
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