The discussion revolves around solving the equation ln(1+e^x)=2 for the variable x, focusing on the manipulation of logarithmic and exponential terms.
The conversation reflects a mix of understanding and confusion regarding the manipulation of logarithmic expressions. Some participants express clarity after receiving feedback, while others continue to seek confirmation on their reasoning.
Participants note the importance of maintaining the natural logarithm in the final answer, indicating a potential misunderstanding of logarithmic properties and their implications in the solution process.
That should be e^ln(1+e^x) = e^2masterchiefo said: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
Take the natural log of both sides !(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
ln(1+e^x)=2SammyS said:That should be e^ln(1+e^x) = e^2
Maybe it's a typo.
Take the natural log of both sides !
The "both sides" refers to the following from your Original Post.masterchiefo said: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?
masterchiefo said:e^x=e^2-1
From the above line to that below,
Take the natural log of both sides !
x ≠ ( e^2-1)
OHH sorry my bad, thank you very much, I understand now :)SammyS said:The "both sides" refers to the following from your Original Post.