fofopausiomiava

2022-09-04

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

Houston Ellis

Hint:
$\mathrm{log}\left(\frac{{x}^{3}}{10y}\right)=\mathrm{log}\left({x}^{3}\right)-\mathrm{log}\left(10\cdot y\right)$
You can use additional properties of logarithms until you get $\mathrm{log}x$ and $\mathrm{log}y$ to appear in your answer. You will need one application each of the properties
$\mathrm{log}\left({a}^{n}\right)=n\mathrm{log}\left(a\right)\phantom{\rule{0ex}{0ex}}\mathrm{log}\left(ab\right)=\mathrm{log}\left(a\right)+\mathrm{log}\left(b\right)$

Gunsaz

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

Do you have a similar question?