Question

Condense as one logarithm: logx-5logy-1/3logz

Answer 1

The first property you need is the power rule. Multiplying a log is the same as raising the quantity inside to the power of what is multiplying.

\[log(x)-log(y^{5})-log(z^{1/3})\]
The next property is of addition/multiplication and subtraction/division.

Adding logs is the same as multiplying the quantities inside the logarithms.
Subtracting logs is the same as dividing the quantities inside the logarithms.

For this reason, you could rewrite what we have as:

\[log(\frac{x}{y^{5}z^{1/3}})\]
Or maybe more nicely without the fraction:
\[log(xy^{-5}z^{-1/3})\]