# Solving Exponential Equations

• Dec 8th 2009, 06:30 PM
Paymemoney
Solving Exponential Equations
Can someone help me solve this equation
$e^x=x+2$

P.S
• Dec 8th 2009, 07:19 PM
mybrohshi5
Are you sure that is the correct problem? Just making sure cause i just took a shot at it and i cannot figure it out....
• Dec 8th 2009, 07:33 PM
Prove It
Quote:

Originally Posted by Paymemoney
Can someone help me solve this equation
$e^x=x+2$

P.S

In short, it can't be solved exactly.

You would have to use Numerical methods like the Bisection Method or Newton's Method.
• Dec 8th 2009, 07:38 PM
mybrohshi5
Quote:

Originally Posted by Prove It
In short, it can't be solved exactly.

You would have to use Numerical methods like the Bisection Method or Newton's Method.

I thought this seemed weird to be in the pre-algebra and algebra section cause i am in calculus and solving this was beyond my knowledge (Rofl)
• Dec 8th 2009, 07:40 PM
Paymemoney
yeh just looked at the question it says you need a graphics calculator to solve this one.
• Dec 8th 2009, 09:01 PM
I-Think
On a random note, a few years of college will teach you how to use the Lambert W function to solve these equations.
Lambert W function - Wikipedia, the free encyclopedia

These types of questions always pop up on the forum once in a while. I'll give links when I have the time.
• Dec 9th 2009, 09:29 AM
I-Think
Here's a link to a similar question that links to another similar question.

http://www.mathhelpforum.com/math-he...nequality.html
• May 25th 2013, 09:55 AM
Yosdam
Re: Solving Exponential Equations
Quote:

Originally Posted by Paymemoney
Can someone help me solve this equation
$e^x=x+2$

P.S

___________-x
1 = (x + 2) e

__
-2___________-x-2
-e__= - (x + 2) e____, where x >= -2

_____________-2
-x-2 = W-1( -e___)

______________-2
x = -2 - W-1( -e___) (x >= -2)

where W-1 is the negative branch of order -1 of Lambert's W function. Go to Lambert W function - Wikipedia, the free encyclopedia to find out how to compute this branch; you can use W-1(x) = ln(-x) - ln(-ln(-x)) or something more complex, depending on the accuracy required
• May 25th 2013, 10:18 AM
MINOANMAN
Re: Solving Exponential Equations
This equation cannot be solved algebraically as it is trancedendal .
you may use graphical methods or numerical ones.
I enclose a graphical one the red line y=x+2 intercepts the blue curve y=e^x at two points...with their coordinates marked in the two figures below.

Attachment 28454

Attachment 28455
• May 25th 2013, 10:42 AM
Yosdam
Re: Solving Exponential Equations
useless and childish