# Thread: simple logs

1. ## simple logs

hi guys how do expand this log expression?

log(3��² √��/³√5��²)

2. Originally Posted by Cockchestner007
hi guys how do expand this log expression?

log(3��² √��/³√5��²)

Doesn't render properly on my system (Vista Home Basic, Firefox).

Image: (click for full size)

3. hey man sorry about it, its

log(3x²√y/³5z²)

4. Originally Posted by Cockchestner007
hey man sorry about it, its

log(3x²√y/³5z²)
I can see all the characters now, but I'm still not sure what it's supposed to be.

Some guesses

$\log\left(\frac{3x^2\sqrt{y}}{\sqrt[3]{5}z^2}\right)$

$\log\left(\frac{3x\sqrt{y}}{\sqrt[3]{5z^2}}\right)$

5. its the first guess!~!!

6. Originally Posted by Cockchestner007
its the first guess!~!!
Applying the rules of logarithms

$\log\left(\frac{3x^2\sqrt{y}}{\sqrt[3]{5}z^2}\right)$

$=\log(3x^2\sqrt{y})-\log(\sqrt[3]{5}z^2)$

$=\log(3)+\log(x^2)+\log(y^{\frac{1}{2}})-\log(5^{\frac{1}{3}})-\log(z^2)$

$=\log(3)+2\cdot\log(x)+\frac{1}{2}\cdot\log(y)-\frac{1}{3}\cdot\log(5)-2\cdot\log(z)$