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Algebra 2 Problem

  1. Apr 18, 2004 #1
    Problem 43.
    Solve and check.
    7^3x divided by 2^7x-1 = (43.2)^x+2
     
  2. jcsd
  3. Apr 18, 2004 #2

    HallsofIvy

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    I am assuming this is that you meant
    [tex]\frac{7^{3x}}{2^{7x-1}}= 43.2^{x+2}[/tex]
    rather than
    [tex]\frac{7^3x}{2^7x-1}= 43.2^x+ 2[/tex]
    which would be harder.

    The key step is to use the logarithm to get rid of the "exponentials" (It really doesn't matter which base logarithm you use):
    [tex]log(\frac{7^{3x}}{2^{7x-1}})= log(43.2^{x+2})[/tex]
    which is:
    [tex] log(7^{3x})- log(2^{7x-1})= log(34.2^{x+2})[/tex]
    [tex] 3x log(7)- (7x-1)log(2)= (x+2)log(34.2)

    That's now a simple linear equation with some peculiar coefficients.
     
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