Write the expression in terms of $\log x$ and $\log y$.

Question

$$\log\Big(\frac{x^3}{10y}\Big)$$ Write the above expression in terms of $\log x$ and $\log y$.

To be honest, I'm really unsure as to how the final answer should look like. In other words, what is the question asking for, and how do I go about getting there?

Any ideas would be appreciated.

Answer 1

Hint: $$\log\left(\frac{x^3}{10y}\right) =\log\left(x^3\right)-\log\left(10\cdot y\right) $$ You can use additional properties of logarithms until you get $\log x$ and $\log y$ to appear in your answer. You will need one application each of the properties $$\log\left(a^n\right) = n\log\left(a\right) \\ \log\left(ab\right) = \log\left(a\right)+\log\left(b\right)$$

Answer 2

$$ \log\left(\frac{x^3}{10y}\right) =3\log x-\log 10-\log y $$ If $\log=\log_{10}$, then $\log 10=1$.