Questions: Find the inverse of (x=e^y).

Find the inverse of (x=e^y).
Transcript text: Find the inverse of $x=e^{y}$.
failed

Solution

failed
failed

Solution Steps

To find the inverse of the function \( x = e^y \), we need to express \( y \) in terms of \( x \). This involves taking the natural logarithm of both sides of the equation to solve for \( y \).

Step 1: Express \( y \) in terms of \( x \)

Given the equation \( x = e^y \), we want to find the inverse function by expressing \( y \) in terms of \( x \). To do this, we take the natural logarithm of both sides:

\[ \ln(x) = \ln(e^y) \]

Step 2: Simplify the Equation

Using the property of logarithms that \( \ln(e^y) = y \), we simplify the equation:

\[ y = \ln(x) \]

Final Answer

The inverse of the function \( x = e^y \) is:

\[ \boxed{y = \ln(x)} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Translate the following phrase into an algebraic expression using the variable w. Do not simplify. the perimeter of a rectangle if the width is w centimeters and the length is 2 cm more than twice the width.
failedAnswered
Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of 28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5v+7f=28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is 2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.) 1.75 2.06 2.39 3.99
failedAnswered
Debbi and Rachel are both in an upcoming school play. When Debbi stops to talk with Rachel about the play after their psychology class, Rachel is preoccupied, thinking about when she is going to see her girlfriend again. Rachel is engaging in which of the following? Multiple Choice glazing over closed-mindedness the rebuttal tendency pseudolistening
failedAnswered
In the yeast experiment measuring CO2 production, your trendline for the tubes in the room temperature water bath gives the equation: y=0.57x+5.86, where time (in minutes) is plotted as the independent variable and distance moved (in mm) is plotted as the dependent variable. How far would the water have moved after 25 minutes? 15.5 mm 20.1 mm 28.8 mm 14.7 mm 5.86 mm
failedAnswered
Solve for y. 5y/4 + 3 = 7y/6 Simplify your answer as much as possible. y=