solve e^3x = 5

Question

solve e^3x = 5

mathmate · Answer

The definition of natural logarithm is:
if $ e^x=a,$ then 
$ x = log_e a $
Plug in values from your equation and evaluate accordingly.

anonymous · Answer

Ok, so would it be 3x = lne5? and since ln and e are one in the same do they cancel leaving it at 3x = 5?

zepdrix · Answer

In mathmate's comment, the e was just a subscript showing the base of the log :)
$$\large 3x=\log_e 5 \qquad\to\qquad 3x=\ln 5$$

anonymous · Answer

Oh...ok. Thank you so much. I get it now.

mathmate · Answer

"and since ln and e are one in the same do they cancel leaving it at 3x = 5?"
I think there is a mix-up with your concept.

$ ln(x) $ is the same as $ log_e(x) $.

However,
$ log_e(e^x) = x $
does not apply to  your case.

anonymous · Answer

Alright. Thank you so it would just be 3x = ln 5?

mathmate · Answer

and consequently solve for x.

anonymous · Answer

Ok so the final result without  a calculator woud be x= ln5/3?

mathmate · Answer

Correct,assuming you mean:
$ \huge x= \frac{ln(5)}{3} $

anonymous · Answer

Yes. Thank you so much.

mathmate · Answer

You're welcome!  :)