help solve: ln(2-ln3x) = 1

Question

tkhunny · Answer

Transform!  Use this $log_{b}(a) = c \iff b^{c} = a$ for suitable a, b, and c.

anonymous · Answer

i did! and it gave me: $$2-\ln3x = e$$
and then i put it to: 
$$2-e = \ln3x$$

what now?! :O

tkhunny · Answer

What's preventing you from doing the same thing?

anonymous · Answer

so, x = 3 / e^2-e  ?

tkhunny · Answer

Well, that's kind of horrible notation.  Add some parentheses and you'll be closer.  Get the division right-side up and you'll be golden.

$2−e=ln(3x) \implies e^{2-e} = 3x \implies x = \dfrac{e^{2-e}}{3}$

anonymous · Answer

oh fail, I've been doing this assignment for 6 hours, I musn't have realized that I did a fail of a division there. thank you for pointing it out.

tkhunny · Answer

No worries.  You were getting it.  No trouble bailing you out after 6 lonely hours.  Can't be there on your exam.  Get enough rest and BE CAREFUL.

anonymous · Answer

thanks :)