Expanding ln isn't working for me

[iScience]

original equation: ln(0.2048x^{[itex]\frac{5}{2}[/itex]})= -[itex]\frac{5}{2}[/itex]

when i just raise this to e i get..

0.2048T^{[itex]\frac{5}{2}[/itex]}= -[itex]\frac{5}{2}[/itex]

and then i can solve for x and get the right answer. but when i expand the logs..

ln(0.2048) + [itex]\frac{5}{2}[/itex]ln(x)= -[itex]\frac{5}{2}[/itex]

0.2048+[itex]\frac{5}{2}[/itex]x=e^{-[itex]\frac{5}{2}[/itex]}

then i try to solve for x i don't get the right answer. what am i doing wrong?

 

[Pythagorean]

you can't do that with a sum of ln's. Taking the exponent of both sides after expansion does not cancel out the ln in each term. You would have e^(lnA + lnB) and that does not equal A+B.

 

[iScience]

oops, lol thanks

 

[Pythagorean]

no problem