Expressing a logarithmic equation

[Random-Hero-]

Homework Statement

http://img142.imageshack.us/img142/8564/76203773.jpg

Homework Equations

I need to somehow express the above equation in terms of log_ax, log_ay,and log_az.

The Attempt at a Solution

I got the answer log_a * [ |x|*sqrt (x)] + log_a * [|y|] - log_a * [z]

But I'd just like to get your guys' opinion, because I have the feeling I'm wrong, lol.

 

[rock.freak667]

How'd you get those answers? Did you use these laws?

$$log_a xy= log_a x + log_a y$$

$$log_ax^r=rlog_a x$$

$$log_a \frac{x}{y} = log_a x - log_a y$$

 

[Mark44]

And your expression (NOT an equation) can be written as
$$\log_a (\frac{x^3 y^2}{z})^{1/2}$$
so you can immediately use the second law that rock.freak667 listed, and continue from there.

 

[HallsofIvy]

Or, not necessary but might help,
$$log_a\left(x^{3/2}yz^{-1/2}\right)$$

 

[Random-Hero-]

Would http://img23.imageshack.us/img23/7739/97409454.jpg be my final answer?

 

[Mark44]

No, for two reasons.

1. It's wrong. The 1/2 factor should multiply all three terms.
2. It can be simplified more in the x and y terms.