# Logs homework

1. Feb 6, 2008

### duki

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

$$ln(6xy)-3ln(2y)-1/3 ln x + ln 20$$

The attempt at a solution

I can get to $$ln\left(\frac{120xy}{8y^3x^1^/^3}\right)$$

And then to

$$ln\left(\frac{120}{8}*\frac{x}{x^1^/^3}*\frac{y}{y^3}\right)$$

But then I am supposed to do something to get to $$ln\left(\frac{15yx^2^/^3}{y^2}\right)$$

What do I do? how does $$\frac{x}{x^1^/^3}$$ turn into $$x^2^/^3$$ and how does $$\frac{y}{y^3}$$ turn into $$y^2$$ ?

2. Feb 6, 2008

### sutupidmath

well x^p/x^q =x^(p-q)

same for y

3. Feb 6, 2008

### duki

o. simple. Thanks :)

4. Feb 7, 2008

### HallsofIvy

Staff Emeritus
Or
$$\frac{y}{y^3}= \frac{y}{y\cdot y\cdot y}= \frac{1}{y\cdot y}= \frac{1}{y^2}$$