# Solving x for ln and e

1. Apr 7, 2015

### math007

1. The problem statement, all variables and given/known data
I need to solve x:
ln (1+e^-x)=-x+2

2. Relevant equations

3. The attempt at a solution
ln (1+e^-x)=-x+2
x+ln (1+1/e^x)=2
x+ln (e^x/e^x+1/e^x)=2
x+ln ((e^x+1)/e^x)=2
x+ln (e^x+1)-ln(e^x)=2
x+ln (e^x+1)-x=2
ln (e^x+1)=2

im stuck here.
thank you

2. Apr 7, 2015

### BiGyElLoWhAt

Perhaps try raising e to both sides of the equation? $e^{lhs}=e^{rhs}$

3. Apr 7, 2015

### math007

sorry I dont really understand.

4. Apr 7, 2015

### BiGyElLoWhAt

ln (e^x+1)=2...
$e^{ln(e^x+1)}=e^2$
...

5. Apr 7, 2015

### BiGyElLoWhAt

In my previous post, lhs was left hand side and rhs was right hand side. That'll come up from time to time, so it wouldn't hurt to keep that in mind.

6. Apr 7, 2015

### math007

where can I read about the rules/ methods to solve ln /e equation because this is confusing me I dont know what to do. :'(

7. Apr 7, 2015

### Staff: Mentor

How would you define the natural log of say a variable called y?

8. Apr 7, 2015

### BiGyElLoWhAt

To add to chet, define it in words, not maths, but of course using some math termonology, such as exponents and whatnot.

9. Apr 7, 2015

### math007

ln (y)?

10. Apr 7, 2015

### BiGyElLoWhAt

yes
define it in words.

11. Apr 7, 2015

### math007

the exponential form of y?

12. Apr 7, 2015

### BiGyElLoWhAt

What is the natural log of y? If I punch $ln(1)$ in my calculator, it returns a 0, why is the answer 0? what does the 0 represent?

13. Apr 7, 2015

### Staff: Mentor

Fill in the blanks: The natural log of y is the power to which you have to raise ____ to get ___.

Chet

14. Apr 7, 2015

### math007

to raise e to get y

ln (e^y)=yln e=y

15. Apr 7, 2015

### BiGyElLoWhAt

Ahhh, so ln(y) is the exponent that I can put on e to get y? So what happens if I take that exponent and stick it on e? what do I get? $e^{ln(y)}=?$

16. Apr 7, 2015

### Staff: Mentor

Good. Now going back to post #4, fill in the blanks: $\ln(1+e^x)$ is the power to which you have to raise ____ to get _____.

Chet

17. Apr 8, 2015

### math007

raise e to get ln (1+e^x)
e^(ln (1+e^x))
then e and ln can cancels? to get 1+e^x

18. Apr 8, 2015

### Staff: Mentor

OK. Good. Now, if you combine this result with the equation in post #4, what do you get for x?

Chet

19. Apr 8, 2015

### math007

e^x+1=e^2
e^x=e^2-1
lne^x=ln (e^2-1)
x=ln (e^2-1)

20. Apr 8, 2015

Excellent!!!