Question

fully expand the logarithm: log(x^3/z^5)

Answer 1

to expand this logarithm, we have to apply the rules. These rules are;

Log(A/B) = logA - LogB and Alogx=log(x∧A)

Log (x³/z∧5) = log (x³) - log z∧5
                    =3log x - 5log z

Answer 2

Using the following properties we can expand the given expression:

1) Quotient Rule of Logs:
Log(A/B) = Log A - Log B

2) Power Rule of Logs: 
$Log(a)^{b}=b*Log(a)$

$log( \frac{ x^{3} }{ z^{5} } ) \\ \\ =log( x^{3})-log( z^{5}) \\ \\ =3logx-5logz$