Help with Adiabatic Derivation

[Identity]

Using $$dU = dW$$,

$$\frac{f}{2}NkdT = -PdV$$

I eventually came to

$$T^\frac{f}{2}V = \mbox{constant}$$

I tried to then get it to the form in the book - $$PV^\frac{f+2}{f}=\mbox{constant}$$ using the formula $$PV = NkT$$:

$$\left(\frac{PV}{Nk}\right)^\frac{f}{2}V=\mbox{constant}$$

$$P^\frac{f}{2}V^\frac{f+2}{2}=\mbox{constant}$$

How do I get it in the right form? Thanks

 

[quydau35]

$$P^{\frac{f}{2}} V^{\frac{f+2}{2}}=const$$
so i have:
$$\frac{f}{2}lnP+\frac{f+2}{2}lnV=constant$$
then:
$$lnP+\frac{f+2}{f}lnV=constant$$

 

[Identity]

Thanks quydau35 :)