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Some tricky exponentioal equations

  1. Nov 27, 2009 #1
    1. The problem statement, all variables and given/known data
    e^(4x-5)=9e^(x+5)


    2. Relevant equations

    log rules

    3. The attempt at a solution

    I have tried this one a few times using slightly different methods and getting 2 answers and neither of them seem to be working when i plug them back into the equation.

    Here is my first method...

    1. Divide out the e^(x+5) so i get e^(4x-5)/e^(x+5) = 9

    2. Take the natural log of everything so i end up with

    (4x-5)lne/(x+5)lne = ln 9

    3. After doing the algebra i got the answer to be 8.87 (rounded to 3 sig figs), but it wasnt checking out when i plugged it back into the equation

    Here is my second method...

    1. I just started going crazy with the natural logs getting

    (4x-5)lne - (x+5) ln 9e

    The ln9e dont quite sit right with me tho, however after doing the algebra i get x=-10, this doesnt seem to check out either...please help!!!

    1. The problem statement, all variables and given/known data

    (3^7x)(27^x)=9

    2. Relevant equations

    logs


    3. The attempt at a solution

    Alright well since i know that they are all powers of 3 i changed the bases so the equation became

    (3^7x)((3^3)x)=3^2

    Then i just looked at the exponents and ended up with

    21x^2 = 2

    Did the algebra and this one isnt working in the orignal equation either >.<
     
    Last edited: Nov 27, 2009
  2. jcsd
  3. Nov 27, 2009 #2
    This part is incorrect. The natural log doesn't quite work like that. Before you take natural logs, you'll want to simplify:
    [tex]
    \frac{e^{4x-5}}{e^{x+5}} = e^{(4x - 5) - (x + 5)} = e^{3x - 10}
    [/tex]
    Then you have e^(3x-10) = 9, and you can take the ln of both sides there.

    Seems a little fishy here. You changed everything to base 3 right, but then you should get:
    [tex]
    3^{7x} \cdot (3^3)^x = 3^{7x} \cdot 3^{3x} = 3^{7x + 3x} = 3^{10x}
    [/tex]

    So then 3^(10x) = 3^2, which means x = ...

     
  4. Nov 27, 2009 #3
    Thank you so much it just clicked..

    I LOVE this site, got my finals right around the corner and this was only problem i was having with exponentioals, thank you i should be able to complete the rest of my assignment with ease :D
     
  5. Nov 27, 2009 #4
    aye, no problem.. good luck!
     
  6. Nov 28, 2009 #5

    Mentallic

    User Avatar
    Homework Helper

    Just be sure to remove that "o" from "exponentioal" if you want full marks :wink:
     
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