Results 1 to 8 of 8

Math Help - Natural Logs - Homework Question

  1. #1
    Newbie
    Joined
    Jun 2011
    Posts
    3

    Natural Logs - Homework Question

    I haven't taken a math class in over a year and a half and am in A Brief Survey of Calculus right now. Our current lesson is over Natural Logs, but I can't seem to figure out how to do this problem. If someone could please show me how to this it'd be amazing!

    5*6^x = 4e^-5x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Natural Logs - Homework Question

    What have you tried so far?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2011
    Posts
    3

    Re: Natural Logs - Homework Question

    I keep taking the natural log of both sides, which will bring both -5x and x down, then divide -5x by x and the x is cancelled out.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Natural Logs - Homework Question

    Ah. Your problem is that the constants on each side of the equation are not raised to a power. How does the logarithm handle multiplication? That is, you have

    \ln(5\cdot 6^{x})=\ln(4e^{-5x});

    what happens to the 5 on the LHS, and the 4 on the RHS?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2011
    Posts
    3

    Re: Natural Logs - Homework Question

    Would you multiply the 5 into the 6? And the 4 into the e? What I end up getting looks like this before I'm lost.

    x*ln7.5 = -5x
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Natural Logs - Homework Question

    Quote Originally Posted by avonscooper View Post
    Would you multiply the 5 into the 6? And the 4 into the e? What I end up getting looks like this before I'm lost.

    x*ln7.5 = -5x
    No, I don't think you've go the idea yet. What is

    \ln(x\cdot y)?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,658
    Thanks
    598

    Re: Natural Logs - Homework Question

    Hello, avonscooper!

    Okay, here it is . . .


    5\cdot 6^x \:=\: 4e^{-5x}

    Take logs: . \ln\left(5\cdot6^x\right) \:=\:\ln\left(4e^{-5x}\right)

    . . . . . . \ln(5) + \ln\left(6^x\right) \:=\:\ln(4) + \ln\left(e^{-5x}\right)

    . . . . . . \ln(5) + x\ln(6) \:=\:\ln(4) - 5x\underbrace{\ln(e)}
    . . . . . . . . . . . . . . . . . . . . . . . . . ^{\text{This is 1}}

    . . . . . . \ln(5) + x\ln(6) \:=\:\ln(4) - 5x

    . . . . . . . . 5x + x\ln(6) \:=\:\ln(4) - \ln(5) \:=\:\ln\left(\tfrac{4}{5}\right)

    . . . . . . . . x[5 + \ln(6)] \:=\:\ln(0.8)

    . . . . . . . . . . . . . . . x \:=\:\frac{\ln(0.8)}{5 + \ln(6)} \:\approx\:-0.032855043

    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1

    Re: Natural Logs - Homework Question

    Quote Originally Posted by avonscooper View Post
    I haven't taken a math class in over a year and a half and am in A Brief Survey of Calculus right now. Our current lesson is over Natural Logs, but I can't seem to figure out how to do this problem. If someone could please show me how to this it'd be amazing!

    5*6^x = 4e^-5x
    You could alternatively try a few simplification steps,
    to get down to a single "x".

    (5)6^x=4e^{-5x}=\frac{4}{e^{5x}}

    6^x=\frac{4}{5e^{5x}}

    6^xe^{5x}=\frac{4}{5}=0.8

    Now use the fact that

    (ab)^c=a^cb^c

    to get

    6^x\left(e^5\right)^x=0.8

    \left(6e^5\right)^x=0.8

    Now you can very simply take logs of both sides to solve for x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: February 22nd 2011, 05:39 PM
  2. Replies: 6
    Last Post: March 18th 2009, 04:10 AM
  3. Dealing with Logs and Natural Logs
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 14th 2008, 06:18 AM
  4. several questions-logs/natural logs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 12th 2007, 08:58 PM
  5. Derivatives of Natural Logs question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 25th 2007, 03:13 PM

Search Tags


/mathhelpforum @mathhelpforum