The inverse of the exponential function

In summary, the inverse of the exponential function is the natural logarithm function, denoted as ln(x). The exponential function and its inverse are inverse relationships, meaning that they "undo" each other's effect. To find the inverse of the exponential function, you can use the property that ln(e^x) = x. The inverse of the exponential function can be negative, as the natural logarithm function can take in any positive number as input and output negative values for values less than 1. The inverse of the exponential function has real-world applications in finance, biology, physics, and chemistry, such as calculating compound interest, modeling population growth, and determining the half-life of radioactive substances.
  • #1
dalterego
14
0
The inverse of the exponential function...

Homework Statement



Find the inverse of the function = e ^ (x^3)

Homework Equations



The inverse of the exponential function = the natural logarithm of that same function

The Attempt at a Solution



inverse of f(x) = ln(x^3) ?

This doesn't seem right.
 
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  • #2


Nope. Let y=e^(x^3). Take Ln of both sides and express x in terms of y. Then replace y with x and you're done.
 
  • #3


Alright, so is the answer

inverse of the function = (ln x)^1/3 ?
 
  • #4


Yeah.
 

1. What is the inverse of the exponential function?

The inverse of the exponential function is the natural logarithm function, denoted as ln(x). It is the function that undoes the effect of the exponential function.

2. What is the relationship between the exponential function and its inverse?

The exponential function and its inverse are inverse relationships, meaning that they "undo" each other's effect. This means that if you apply the exponential function to a number, and then apply the natural logarithm function to the result, you will get back the original number.

3. How do you find the inverse of the exponential function?

To find the inverse of the exponential function, you can use the property that ln(e^x) = x. In other words, the inverse of the exponential function is the natural logarithm function.

4. Can the inverse of the exponential function be negative?

Yes, the inverse of the exponential function can be negative. The natural logarithm function can take in any positive number as input, and its output can be negative for values less than 1.

5. What are some real-world applications of the inverse of the exponential function?

The inverse of the exponential function is used in many fields including finance, biology, physics, and chemistry. Some examples include calculating compound interest, modeling population growth, and determining the half-life of radioactive substances.

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