Natural Logs and inverse functions

In summary, to find the inverse equation of y = (e^x)/(1 + 2e^x), we can start by multiplying both sides by (1 + 2e^x) and then rearranging the terms to isolate x. We can then factor out e^x and divide both sides by the remaining factor to solve for x.
  • #1
b200w
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0

Homework Statement


Find the inverse equation (i.e. solve for x)
y=(e^x)/(1+2e^x)2. The attempt at a solution
e^x = y(1+2e^x)
x = ln(y) + ln(1+2e^x)
?
Profit!

I can't figure out what to do with ln(1+2e^x) to get the x out of there so I can finish isolating x. I tried balancing it another way and ended up with x = ln(e^x - y) - ln(2y) which as far as I can tell is worse. Any suggestions? As far as I can tell I'm probably just missing something obvious but I've been sitting here for a while trying to figure it out...
 
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  • #2
Starting with y = e^x/(1 + 2e^x),
multiply both sides by (1 + 2e^x).

Get all the terms that involve e^x on one side, and all other terms on the other side.
Factor e^x out of the terms that have this factor and divide both sides by the factor that isn't e^x.
 
  • #3
*facepalm* Thank you... I don't know why I couldn't figure that out...
 

Related to Natural Logs and inverse functions

1. What is a natural log?

A natural log, or ln, is a mathematical function that is the inverse of the exponential function. It is the logarithm to the base e, where e is a mathematical constant approximately equal to 2.71828.

2. What is the difference between a natural log and a regular logarithm?

The main difference is the base of the logarithm. A regular logarithm uses a base of 10, while a natural log uses a base of e. Additionally, a natural log is the inverse of the exponential function, while a regular logarithm is the inverse of the power function.

3. How do you solve for a natural log?

To solve for a natural log, you can use the inverse property of logarithms. This means that if ln(x) = y, then e^y = x. You can also use a calculator to find the value of a natural log.

4. What is the domain and range of a natural log?

The domain of a natural log is all positive real numbers, while the range is all real numbers. This means that the input of a natural log must be positive, but the output can be any real number.

5. How are natural logs used in science?

Natural logs are used in a variety of scientific fields, such as biology, chemistry, physics, and economics. They are often used to model exponential growth and decay, which can be found in various natural processes. They are also used in statistical analysis and data modeling.

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