Condensing logarithmic expressions

Question

See attached images. Not sure where I'm going wrong.

Answer 1

First of all remember that $\sqrt[n]a=a^{1/n}$. So $$4\log_6\sqrt y=\log_6 (y^{1/2})^4=\log_6 y^2.$$ Now your final line in the first problem is

$$\log_6 {(x-2)^2/z^3\over y^2}.$$

$${(x-2)^2/z^3\over y^2}={(x-2)^2\over z^3}\cdot\frac1{y^2}={(x-2)^2\over y^2z^3}.$$

Final answer:

$$\log_6 {(x-2)^2\over y^2z^3}.$$

You should be able to figure out the second question in a similar manner.