1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Natural logarithm equation

  1. Mar 4, 2013 #1
    Solve the following equation for x


    I know I need to isolate x . however I am unsure how to get ln(7x) separated.

    what i have so far

  2. jcsd
  3. Mar 4, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    e^(ln(y)) = y

    e = 2.71828...
  4. Mar 5, 2013 #3


    User Avatar
    Science Advisor

    You always solve an equation for a variable such as x by doing the reverse of what has been done to it (to both sides, of course).

    If you were asked to evaluate 23- 9ln(4x) (I am using different numbers so you can apply the same idea to your problem) for a given value of x, you would:
    1) multiply by 4: 4x.
    2) take the natural logarithn: ln(4x)
    3) multiply by -9: -9 ln(7x)
    4) add 23: 23- 12 ln(7x)

    To solve for x, do the opposite: do the opposite of each step, in the opposite order. The opposite of "add 23" is "subtract 23", the opposite of "multiply by -9" is "divide by -9", the opposite of "multiply by 4" is "divide by 4", and the opposite of "take the natural logarithm" is "take the exponential".

    Starting from 23- 9 ln(4x)= 85:
    1) subtract 23: 23- 9ln(4x)- 23= 84- 23, -9ln(4x)= 61
    2) divide by -9: -9ln(4x)/(-9)= 61/(-9), ln(4x)= -61/9
    3) take the exponential: eln(4x)= e-61/9: 4x= e- 61/9[/tex]
    4) divide by 4: 4x/4= e-61/9/4, x= e-61/9/4.

    You will need to use a calculator to actually evaluate e-61/9.
    Last edited by a moderator: Mar 5, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted