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Math Help - Solve for x

  1. #1
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    Solve for x

    Solve for x. Question1. ln(x^5) - ln(x^3) = 2.4 Question2. 2[ln(x^2+4)]=3.9
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  2. #2
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    Hello, oldschool999!

    Solve for x.

    1)\;\;\ln(x^5) - \ln(x^3) \:= \:2.4
    Combine logs: . \ln\left(\frac{x^5}{x^3}\right) \:=\:2.4

    Simplify: . \ln(x^2) \:=\:2.4

    Convert: . x^2 \:=\:e^{2.4}\quad\Rightarrow\quad x^2 \:=\:11.02317638

    Therefore: . x\:=\:\sqrt{11.02317638} \:=\:3.320116923



    2)\;\;2\ln(x^2+4) \:=\:3.9

    Divide by 2: . \ln(x^2+4) \:=\:1.95

    Convert: . x^2+4 \:=\:e^{1.95}\quad\Rightarrow\quad x^2+4 \:=\:7.02868758

    Subtract 4: . x^2 \:=\:3.028687581

    Therefore: . x\:=\:\sqrt{3.028687581} \:=\:1.740312495

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