# Expressing a logarithmic equation

1. Jun 3, 2009

### Random-Hero-

1. The problem statement, all variables and given/known data

http://img142.imageshack.us/img142/8564/76203773.jpg [Broken]

2. Relevant equations

I need to somehow express the above equation in terms of logax, logay,and logaz.

3. The attempt at a solution

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

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

Last edited by a moderator: May 4, 2017
2. Jun 3, 2009

### rock.freak667

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

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

$$log_ax^r=rlog_a x$$

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

3. Jun 4, 2009

### Staff: Mentor

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.

4. Jun 4, 2009

### HallsofIvy

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

5. Jun 4, 2009

### Random-Hero-

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

Last edited by a moderator: May 4, 2017
6. Jun 4, 2009

### Staff: Mentor

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.