Solving Complex Logarithmic Equations

[duki]

Homework Statement

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

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 $$y^2$$ ?

 

[sutupidmath]

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

same for y

 

[duki]

o. simple. Thanks :)

 

[HallsofIvy]

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