Just follow the log properties:
[tex]n \ln (a) = \ln (a^n) \\ \ln a + \ln b = \ln (ab) \\ \ln a - \ln b = \ln (\frac{a}{b})[/tex]
First make all the coefficients exponents inside each log:
[tex]\ln x^2 + \ln y^3 -\ln z^{1/2}[/tex]
Then combine, if following addition sign, multiply. If following subtraction sign, put in denominator inside log.
[tex]\ln (\frac{x^2 y^3}{z^{1/2}})[/tex]
