May I know what is e and ln,how to apply it to this 5^x=9

Question

e.mccormick · Answer

e is a constant... it is like $\pi$ in some respects.  They represent numbers that never end.
ln is shorthand for $\log_e$ or log to the base of e.

Because it is log base e, $\ln e=1$ and  $\ln e^x\implies x \ln e=x$ and

e.mccormick · Answer

For $5^x=9$ I would not use ln or e, but I would use logs. This talks about it: http://www.regentsprep.org/regents/math/algtrig/ATE8/exponentialEquations.htm The second set of examples, right at the top.

anonymous · Answer

So,when only should I use e and ln?

e.mccormick · Answer

Or not necessary use ln to be more clear.  You can use log as well.  For change of base stuff, like what your first one is, either ln or log will work.  I would use whichever one your calculator does easiest.

You need to use e if you are trying to solve ln of something:

$\ln x = 5$
$e^{\ln x} = e^5$
$x = e^5$

anonymous · Answer

Ah,understood.Thanks :)

e.mccormick · Answer

np.  And like I said, take a look at the examples on that page.  They show it several times with solutions and steps.  They short hand it, but it should help you to see them use it.

e.mccormick · Answer

Well, time to get some sleep...  have fun!

anonymous · Answer

Alright,will do.