How Do You Solve \( e^{x-1} = 5 - y^2 + y \) for x?

  • Thread starter masterchiefo
  • Start date
In summary, to solve the equation ex-1=5-y2+y for x, take the natural logarithm of both sides to get x=ln(5-y2+y)+1. However, it is important to note that the equation only holds if y satisfies an inequality regarding its values.
  • #1
masterchiefo
212
2

Homework Statement


Solve e x-1 = 5-y2+y for x

Homework Equations


/

The Attempt at a Solution


ln(ex-1)=ln(5-y2+y)
x-1=ln(5-y2+y)
x=ln(5-y2+y)+1

can I go any further ?
 
Last edited:
Physics news on Phys.org
  • #2
Nope, just mind one thing, you have to include a constraint that 5-y2+y>0 which holds only if y satisfies an inequality regarding its values.

Btw i just noticed one small "typo", it should be x=ln(..)+1 not -1...
 
  • #3
Delta² said:
Nope, just mind one thing, you have to include a constraint that 5-y2+y>0 which holds only if y satisfies an inequality regarding its values.

Btw i just noticed one small "typo", it should be x=ln(..)+1 not -1...
thank you very much for the help man :)
oops fixed that typo
 

FAQ: How Do You Solve \( e^{x-1} = 5 - y^2 + y \) for x?

What is e?

e is a mathematical constant approximately equal to 2.71828. It is the base of the natural logarithm and is often used in scientific calculations.

How do I solve an equation with e?

To solve an equation with e, you can use logarithms. In this case, taking the natural logarithm of both sides of the equation will help isolate the variable x.

What is the natural logarithm?

The natural logarithm, denoted as ln, is the inverse function of the exponential function with base e. It is commonly used in mathematical and scientific calculations.

Can I use a calculator to solve this equation?

Yes, you can use a scientific calculator to solve this equation. You can use the natural logarithm function on the calculator to find the value of x.

Are there any special rules for solving equations with e?

Yes, there are some special rules to keep in mind when solving equations with e. One important rule is that e raised to the power of 0 is equal to 1. Additionally, e raised to any negative power is equal to 1 divided by e raised to the positive version of that power.

Back
Top