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.
The "ln(1+e^x)=2" problem is a logarithmic equation that involves solving for the value of x. It is commonly used in mathematics and science, particularly in calculus and differential equations.
To solve the "ln(1+e^x)=2" problem, you can use the properties of logarithms to rewrite the equation as e^x = e^2 - 1. Then, take the natural logarithm of both sides to isolate the x variable. The final solution will be x = ln(e^2 - 1).
The "ln(1+e^x)=2" problem is important in science because it is used to model various natural phenomena, such as population growth, radioactive decay, and chemical reactions. It also has applications in fields such as physics, economics, and biology.
One common mistake when solving the "ln(1+e^x)=2" problem is forgetting to apply the properties of logarithms correctly. Another mistake is not isolating the x variable and trying to solve for e^x instead. It is also important to check for extraneous solutions, as the natural logarithm function is only defined for positive values.
Yes, you can use a calculator to solve the "ln(1+e^x)=2" problem. Most scientific calculators have a natural logarithm function (usually denoted as "ln" or "log"). However, it is always important to check your answer by plugging it back into the original equation to ensure it satisfies the solution.