Question

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

Answer 1

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( ( x^(3) )/( z^(5) ) ) \\ \\ =log( x^(3))-log( z^(5)) \\ \\ =3logx-5logz`

Answer 2

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