How do I solve exponentials with base e?

  • Thread starter LinkMage
  • Start date
  • #1
LinkMage
18
0
I don't know how to solve x for things like e^x=20.
The problem I have to solve is x^3+e^(2x)+8=0
Can anyone help, please?
 

Answers and Replies

  • #2
zwtipp05
107
0
have you learned logarithms?

what is the natural log of e^x?
 
  • #3
Tide
Science Advisor
Homework Helper
3,089
0
LinkMage said:
I don't know how to solve x for things like e^x=20.
The problem I have to solve is x^3+e^(2x)+8=0
Can anyone help, please?

You won't be able to find an exact solution to your problem so you will have to resort to solving it graphically or by iteration.
 
  • #4
Ouabache
Science Advisor
Homework Helper
1,343
8
The exponential function is the inverse function of the natural logarithm.
therefore [tex] ln(e^{f(x)}) = f(x)[/tex]. In your example, like any equation, what you do on one side of the equation must be done on the other side. You can take the natural log of both sides [tex]ln(e^{x})=ln(20) [/tex]
Then using the property I gave above you should be able to solve for x

Once you have practised using the idea given above, you can then tackle your second question. You may want to bring your x-terms on one side of equation and any other terms, to the other side of equation. As with the first query, take the natural log of both sides. Though you eliminate your exponential function, you may still have some natural log terms left. That's okay, by substitution of values for x you should arrive at correct value f(x) to your question.

Edit: By plotting the values of x you substitute and resulting values f(x), as Tide suggests; by observing the trend in your graph, you may find (or at least narrow down) your solutions more quickly.
 
Last edited:
  • #5
LinkMage
18
0
You mean I just replace values for x until I get that the equation equals 0. That's what I did first and got aproximately -2.001. I was just wondering if I could solve the equation instead of replacing numbers.
 
  • #6
Jameson
Gold Member
MHB
4,538
13
Anytime you have a logarithm, there are different rules that you need to know. For the first example you gave the one you need to know is this.

[tex]\log_{a}b^c=c\log_{a}b[/tex] it also follows that

[tex]\ln a^b=b\ln a[/tex]

So when you are given something like [tex]e^x=20[/tex], how can you apply this rule to solve that?

For your second problem, as others have said, you cannot solve for x explicity so another method must be used.
 
  • #7
djeipa
46
0
zwtipp05 said:
have you learned logarithms?

what is the natural log of e^x?
it is equal to x,

well, I just wanted to remind theOP
 

Suggested for: How do I solve exponentials with base e?

Replies
18
Views
448
Replies
3
Views
564
Replies
4
Views
366
Replies
19
Views
479
Replies
13
Views
434
  • Last Post
Replies
15
Views
533
Replies
9
Views
126
Replies
3
Views
315
Top