ln(-5x+3)=ln2x+2

Question

ln(-5x+3)=ln2x+2

anonymous · Answer

Do I cancel out the ln's?

anonymous · Answer

@hartnn

hartnn · Answer

whats the question ? 
$\ln (-5x+3)=\ln 2x+2$
or 
$\ln (-5x+3)=\ln (2x+2)$
?

anonymous · Answer

The top one

hartnn · Answer

then you cannot cancel and its not an easy Q

anonymous · Answer

Then what do you do?

hartnn · Answer

i would use these 2,
$\ln A=B \implies A=e^B$
and 
$\large e^{\ln A}=A$

hartnn · Answer

first,
$\huge (-5x+3)=e^{\ln 2x+2}$
got this ?

anonymous · Answer

One quick question, would you treat ln like log?

hartnn · Answer

yes, ln is log only, but with different base
log --->base = 10 
ln ----> base = e
all properties of log applies to both

anonymous · Answer

Would there be another way to write the first step?

hartnn · Answer

i can't think of other...i already said this wasn't going to be easy...and complications haven't even started yet :P

anonymous · Answer

Haha, alright

hartnn · Answer

let me put down steps to let u know 
$\huge (-5x+3)=e^{\ln 2x}\times e^2  \ -5x+3 = 2x (e^2) \ x (2e^2 +5)=3 \ x= \dfrac{3}{2e^2+5}$
all these just because there were no brackets on right side... :P

hartnn · Answer

if there were brackets on right side, then u could have cancelled ln 
and it would be as simple as 
-5x+3=2x+2

hartnn · Answer

any doubts ?

anonymous · Answer

I'll try to process that in my brain :P

hartnn · Answer

okk. i got to go, bye :)