Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By topsquark
  • 1 Post By HallsofIvy

Math Help - Variable in exponent

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Unreals
    Posts
    48

    Variable in exponent

    Hi!

    Solve e^{2x} = 3^{x - 4}

    I have used \log_3 but this is where it leads:

    \log_3 e^{2x} = \log_3 3^{x-4}

    2x \log_3 e = x - 4

    2x \log_3 e + 4 = x

    \frac{\log_3 e + 4}{2} = \frac{x}{2x} = \frac12
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1

    Re: Variable in exponent

    Quote Originally Posted by Unreal View Post
    Hi!

    Solve e^{2x} = 3^{x - 4}

    I have used \log_3 but this is where it leads:

    \log_3 e^{2x} = \log_3 3^{x-4}

    2x \log_3 e = x - 4

    2x \log_3 e + 4 = x

    \frac{\log_3 e + 4}{2} = \frac{x}{2x} = \frac12
    What happened in that last line?

    2x \log_3 e + 4 = x

    2x \log_3 e - x = -4

    Now factor the x on the LHS and solve.

    -Dan
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,419
    Thanks
    1855

    Re: Variable in exponent

    Quote Originally Posted by Unreal View Post
    Hi!

    Solve e^{2x} = 3^{x - 4}

    I have used \log_3 but this is where it leads:

    \log_3 e^{2x} = \log_3 3^{x-4}

    2x \log_3 e = x - 4

    2x \log_3 e + 4 = x
    This is correct up to here although I think it would have been better to take the logarithm with respect to e, not 3, getting
    2x= (x+ 3) ln(3) just because you can easily find a numerical value for log(3). But, as I say, what you have done is correct to this point.

    \frac{\log_3 e + 4}{2} = \frac{x}{2x} = \frac{1}{2}
    But here you have gone wrong. Dividing the left side by "2x" leaves log_3(e)+ \frac{2}{x}= \frac{1}{2}

    Subtract log_3(e) from both sides to get \frac{2}{x}= \frac{1}{2}- log_3(x) and then, since "x" is in the denominator on the left, take the reciprocal of both sides:
    \frac{x}{2}= \frac{1}{\frac{1}{2}- log_2(x)}

    x= \frac{2}{\frac{1}{2}- log_3(e)}
    Last edited by HallsofIvy; April 29th 2013 at 08:42 AM.
    Thanks from Unreal
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding an exponent variable.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 29th 2011, 11:52 PM
  2. LImit with and exponent variable
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 26th 2011, 07:49 PM
  3. Solve for variable exponent...
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 29th 2009, 11:44 PM
  4. variable in the exponent
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 4th 2009, 05:46 AM
  5. X variable in exponent, solve for x
    Posted in the Algebra Forum
    Replies: 16
    Last Post: December 17th 2008, 10:29 AM

Search Tags


/mathhelpforum @mathhelpforum