Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

the equation is

$\ln(x+2)=\ln e^{\ln2} - \ln x$

How do I solve for $x$?

share|cite|improve this question
$e^{\ln 2} = 2$, for starters – The Chaz 2.0 Oct 23 '13 at 4:03
can you explain why ? – user293849 Oct 23 '13 at 4:26
@user293849: Think about it: What does "$\ln 2$" mean? – Blue Oct 23 '13 at 4:27
@user293849 Look up the logarithm identities $\ln a^b = b \ln a$. In your case $b=\ln 2$ and $\ln e=1$. Please have a look here – triomphe Oct 23 '13 at 4:32

Your equation is equivalent to $$\ln (x+2)+\ln(x)=\ln2.$$ Then use logarithm identity $\ln ab=\ln a +\ln b$\$ $$\ln (x+2)x=\ln2.$$ Now take inverse of both sides $$(x+2)x=2.$$ Now you can solve the quadratic equation and select the appropriate $x$ value. You get $x=-1\pm\sqrt 3.$ Note that you can not take $x<0$ as $\ln x$ is not defined for negative $x$. So your answer is $x=-1+\sqrt 3$ which is approximately equal to $0.732$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.