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Exponential equation

  1. Jul 5, 2010 #1

    DTA

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

    Solve for x:

    4x+7=18

    2. Relevant equations

    It becomes 4x=11

    3. The attempt at a solution

    I have no idea where to go from here. We never had a problem with such an immovable number such as 11 to work with. Calculators are not allowed to be used either.
     
  2. jcsd
  3. Jul 5, 2010 #2
    Use the definition of a logarithm.
     
  4. Jul 5, 2010 #3

    DTA

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    Okay, I think I'm on the right track but I'm still not sure where to go with this:

    4log411= ?
     
  5. Jul 5, 2010 #4
    For logarithms it is always true that:

    [tex]
    a^{x} = b \Leftrightarrow x = \log_{a}{b}, \; a, b > 0, \; a \neq 1
    [/tex]

    From here we have the fundmanetal property of logarithms:

    [tex]
    a^{\log_{a} b} = b
    [/tex]
     
  6. Jul 5, 2010 #5

    LCKurtz

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    Take the log of both sides to any base and solve for x. It doesn't have to be base 4 and if you were after a decimal approximation you would likely want to use base e or base 10.
     
  7. Jul 6, 2010 #6

    DTA

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    Okay, so I attempted a change of base and got this:

    ln11/ln4 ~ 1.729

    Is this how it eventually would end up?


    Thanks for all your help! Logarithms are just driving me nuts for some reason
     
  8. Jul 6, 2010 #7
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