Rewriting Equations with ln and Exponential Terms

[masterchiefo]

Homework Statement

I have to solve ln(1+e^x)=2 for x

Homework Equations

The Attempt at a Solution

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

The real answer is x=ln(e^2-1) but I don't understand why we have to put the ln back? why can't we keep it like that x=(e^2-1).

thank you very much

 

[SammyS]

Homework Statement

I have to solve ln(1+e^x)=2 for x

Homework Equations

The Attempt at a Solution

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

That should be e^ln(1+e^x) = e^2

Maybe it's a typo.

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

Take the natural log of both sides !

x=(e^2-1)

The real answer is x=ln(e^2-1) but I don't understand why we have to put the ln back? why can't we keep it like that x=(e^2-1).

thank you very much

 

[masterchiefo]

That should be e^ln(1+e^x) = e^2

Maybe it's a typo.

Take the natural log of both sides !

ln(1+e^x)=2
ln(1+e^x)=lne^2 -- forgot to add the ln there.
then I take out ln on both side then at the end I basically have to add ln back to reduce it to x?

 

[SammyS]

ln(1+e^x)=2
ln(1+e^x)=lne^2 -- forgot to add the ln there.
then I take out ln on both side then at the end I basically have to add ln back to reduce it to x?

The "both sides" refers to the following from your Original Post.

e^x=e^2-1

From the above line to that below,

Take the natural log of both sides !​

x ≠ ( e^2-1)

 

[masterchiefo]

The "both sides" refers to the following from your Original Post.

OHH sorry my bad, thank you very much, I understand now :)