Question

ln(x+2)=3
I know solving this is relatively simple, but I can't seem to remember the steps... :(

Answer 1

e^ both sides.

Answer 2

x+2=e^3

Answer 3

e^ln(x+2)=e^3
x+2 =e^3

Answer 4

Ohh! Wow, yes. I remember that now. Thank you so much!

Answer 5

Yeah after a while you forget things if you stop doing them.

Answer 6

Unfortunately :/ And logs/natural logs just never seemed to be my thing anyway!

Answer 7

logs and natural logs have the same rules, the difference is that natural log has base "e" and log has 10

you could have solved this using one of these rules:

\[\LARGE \ln_e(x)=b\quad \quad ,\quad \quad x=e^b\]
or raising both sides in power like
\[\LARGE e^{ln_e(x)}=e^3\]
here the left side would get rid of with the formula

\[\LARGE e^{ln_e(a)}=a\]
that's the same with logs too...

Answer 8

Thank you, Kreshnik! I'll be sure to write those down for future reference (:

Answer 9

Oops, I actually have another similar question! 10^2x=500
Should I take the log of both sides here? Or...?

Answer 10

@Romero ! I need your help again!

Answer 11

On ?

Answer 12

If you have another problem just post another question.

Answer 13

@AgentNao sorry for late respoinding...I was in school.
\[\LARGE 10^{2x}=500 \]
and yes we take logs to both sides to get "x" down...
\[\LARGE \log_{10}(10)^{2x}=\log_{10}(500 )\]
now according to this rule:
\[ \LARGE \log_a(b^c)=c\cdot \log_a(b)\]
we have: (left side...)
\[ \LARGE 2x\cdot \log_{10}(10)=\log_{10}(10\cdot 10\cdot 5 )\]
now for the left side we have to use this formula:
\[\LARGE \log_a(a)=1\]
and for the right side we use:
\[\LARGE \log_a(b)+\log_a(c)=\log_a(b\cdot c )\]
and vice versa... so...
\[\LARGE 2x\cdot 1=\log_{10}(10)+\log_{10}(10)+\log_{10}(5)\]
and applying again rule:
\[\LARGE \log_a(a)=1\quad \quad \text{(Right Side...)}\]
we would have:
\[\LARGE 2x=1+1+\log_{10}(5)\]
knowing (by calculator) that \(\LARGE \log_{10}(5)\approx 0.69 \)
it's easy to find X... Good luck !

... and also you might wanna check this for more "basic rules" with logs and something else...
http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet.pdf