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Math Help - Logarithmic Question: Completed, Incorrect Answer

  1. #1
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    Logarithmic Question: Completed, Incorrect Answer

    Hi,

    How do I solve  4(7^{x+2})=9^{2x-3} ?

    If I take the natural logarithm of both sides:

     ln (4(7^{x+2})=ln(9^{2x-3}) , and bringing the exponents in front of the expressions:

     (x+2)ln(4(7)) = (2x-3)ln(9) \to \frac{x+2}{2x-3}=\frac{ln(9)}{ln(28)}

    Where do I go from here or have I done this correctly?

     \frac{x+2}{2x-3}=0.6594 \to (2x - 3)(0.6594) = x + 2 \to 1.3188x -1.9782 = x + 2 \to .3188x = 3.9782 \to x = 12.4787

    Where have I gone wrong?

    Thanks!
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  2. #2
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    Re: Logarithmic Question: Completed, Incorrect Answer

    Quote Originally Posted by SC313 View Post
    How do I solve  4(7^{x+2})=9^{2x-3} ?

    Oh come on?
    \ln(4\cdot 7^{x+2})=\ln(4)+(x+2)\ln(7)

    If you know anything about logarithms, you should know that.
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