1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Exp. Equation

  1. Jan 12, 2006 #1
    [tex]e^{2x + 1} = 5[/tex]

    How can I solve this without a calculator?
  2. jcsd
  3. Jan 12, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    Do you need a number or an expression as an answer?
  4. Jan 12, 2006 #3
    For the other parts of the question I've been able to find a numerical answer so I assume I should be finding one for this one, but is it possible without a calculator?
  5. Jan 12, 2006 #4
    Not unless you can do ln(5) in your head or somehow...:uhh: Usually an expression is enough, depends on how it's being marked though.
  6. Jan 12, 2006 #5
    Well I get [tex]x=\frac{\ln(5)-1}{2}[/tex]. That doesn't have an exact decimal representation, so you can leave it in exact form or approximate.
  7. Jan 12, 2006 #6
    Ah ok, thanks.
  8. Jan 12, 2006 #7


    User Avatar
    Homework Helper

    The method of solution is as follows:

    Given [tex]e^{2x + 1} = 5,[/tex]

    take the ln of both sides,

    [tex]\ln \left( e^{2x + 1}\right) = \ln (5),[/tex]

    recall that [itex]\ln \left( a^{x}\right) = x\ln \left( a\right) [/itex], so we have

    [tex](2x + 1)\ln \left( e\right) = \ln (5),[/tex]

    and since [itex]\ln \left( e\right) = 1 [/itex], we have

    [tex](2x + 1)(1) = \ln (5),[/tex]


    [tex]x=\frac{1}{2}\left( \ln (5) -1\right) [/tex]
  9. Jan 12, 2006 #8


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Sure it does!

    Of course, I know you meant one that we can write with finitely many digits... but I don't want this to perpetuate the myth that decimal expansions do not exactly represent real numbers.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Exp. Equation
  1. Ln(y) and exp(y) :S (Replies: 2)

  2. System of equations (Replies: 8)

  3. Linear equations (Replies: 3)