• Support PF! Buy your school textbooks, materials and every day products Here!

Exponential equation

  • Thread starter cue928
  • Start date
  • #1
130
0
e^2x = 5e^3x


I understand that I need to take a natural log of both sides here, what I am thrown about is the constant "5". Can I bring that up as an exponent? So, e^2x = e^(3x)^5?
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
14
No, not really. That's a rule for logarithms, not for exponents.

However, it's not really a problem. Once you take the natural log of both sides, you just need to remember a different logarithm rule:

[tex]log(ab)=log(a)+log(b)[/tex]

That's all you need here.
 
  • #3
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
132
You might also rewrite this equation, dividing with 5e^2x on both sides:
e^x=1/5
 
  • #4
130
0
Sorry but I don't completely follow. I get that I need to take a natural log of both sides, so are you saying: ln(e^2x) = 5 ln(e^2x)?
 
  • #5
Char. Limit
Gold Member
1,204
14
Sorry but I don't completely follow. I get that I need to take a natural log of both sides, so are you saying: ln(e^2x) = 5 ln(e^2x)?
No, I'm saying that ln(e^2x)=ln(5e^(3x)). From there, you can use the logarithm rule I posted above to separate the 5.
 
  • #6
130
0
No, I'm saying that ln(e^2x)=ln(5e^(3x)). From there, you can use the logarithm rule I posted above to separate the 5.
Thanks, got it!
 

Related Threads on Exponential equation

  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
1
Views
1K
Top