Question

ln3x=5...plz help!

Answer 1

im not sure if it's \[\frac{ \ln5 }{ \ln3 }\]

Answer 2

Use 'e' when getting rid of ln

Answer 3

e is your friend.

Answer 4

i love e, i just don't know how to use him to his full extent..

Answer 5

\[\large e^{\ln(3x)}=3x\]

Answer 6

Make sure you e both sides

Answer 7

What do you get?

Answer 8

um..\[e^\ln(3x) = e^3x\] ?

Answer 9

More generally:
\(e^{ln(anything)}=anything\) and conversely \(ln^{e^{anything}}=anything\)

Answer 10

ahh

Answer 11

I meant \(ln(e^{anything})=anything\) on the second part.

Answer 12

From
\[\ln(3x)=5 \]
e both sides you get
\[e^{\ln(3x)}=e^5 \\ \\\]
\[3x=e^5\]

Answer 13

im not sure that can be th final answer...

Answer 14

Well, he did not divide through by 3.... But it is that close to the final answer.

Answer 15

kk

Answer 16

Remember that e is just a number, not a rational one, but it is real enough. So \(\frac{e^5}{3}\) is a real solution.

Answer 17

wow, okay..thx!

Answer 18

Now, if someone asks for a rational, integer, etc. solution, e is no longer your friend. e becomes that guy you know down the street who hangs out what odd crowd, \(\pi\) and the \(\sqrt2\).