Logarithim Help Gas Laws

[Corbeau_dubh]

Spinning my head up side down trying to work this out. Any help would be greatly appreciated. I imagine it's just using the basic laws of logs but I'm just missing it.

The pressure, ?, and volume, ?, of a gas are related by

ln?=−?ln?+ln?

where ? and ? are constants. Show that,

ln???=ln?

 

[HallsofIvy]

Yes, you need to use the basic "laws of logarithms":
log(ab)= log(a)+ log(b)
log(a^n)= n log(a) and
if log(a)= log(b) then a= b.

-nlog(V)= log(V^{-n})= log(1/V^n) and then -nlog(V)+ log(C)= log(C/V^n) so log(P)= log(C/V^n) and then P= C/V^n. (NOT "Vn"!)

 

[Corbeau_dubh]

Yes, you need to use the basic "laws of logarithms":
log(ab)= log(a)+ log(b)
log(a^n)= n log(a) and
if log(a)= log(b) then a= b.

-nlog(V)= log(V^{-n})= log(1/V^n) and then -nlog(V)+ log(C)= log(C/V^n) so log(P)= log(C/V^n) and then P= C/V^n. (NOT "Vn"!)

Yes it was the -n that threw me off. Just had to make it the transponent of V. Thank you so much for your help