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Thread: Solve for x

  1. #1
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    Solve for x

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

    Solve for x.

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

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

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

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



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

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

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

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

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

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