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Math Help - Please solve equation

  1. #1
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    Please solve equation

    Is the correct answer x = (5 ln 3 - 2 ln 4) : (ln 4-2 ln3)
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  2. #2
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    Yes, if you don't want to simplify further.
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  3. #3
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    How do you further simplify it? You mean to calculate on the calculator? Or is there another way? I am going to do it, I wanted to make sure that I solved it right. Thank you for your help.
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  4. #4
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    How do you further simplify it? You mean to calculate on the calculator? Or is there another way? I am going to do it, I wanted to make sure that I solved it right. Thank you for your help.
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  5. #5
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    Quote Originally Posted by oceanmd View Post
    How do you further simplify it? You mean to calculate on the calculator? Or is there another way? I am going to do it, I wanted to make sure that I solved it right. Thank you for your help.
    4^(x +2) = 3^(2x +5)
    (x +2)ln(4) = (2x +5)ln(3)
    x*ln(4) +2ln(4) = 2x*ln(3) +5ln(3)
    x[ln(4) -2ln(3)] = 5ln(3) -2ln(4)
    x = [5ln(3) -2ln(4)] / [ln(4) -2ln(3)] ------your solution.

    If you want to go on simplifying that, here is one way,
    x = [ln(3^5) -ln(4^2)] / [ln(4) -ln(3^2)]
    x = [ln(243) -ln(16)] / [ln(4) -ln(9)]

    Since ln(a/b) = ln(a) -ln(b), then,

    x = [ln(243/16)] / [ln(4/9)] --------------answer.

    By calculator,
    x = -3.354755646
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