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Math Help - [SOLVED] natural logarithms

  1. #1
    barb
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    [SOLVED] natural logarithms

    i am very confused and i need help solving this equation. thanks.

    4 ln 2x=ln e^2
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  2. #2
    Super Member

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    Hello,barb!

    4\!\cdot\!\ln(2x) \:= \:\ln\left(e^2\right)
    First of all: . \ln(e^2) \;=\;2

    So we have: . 4\!\cdot\!\ln(2x) \;=\;2

    Divide by 4: . \ln(2x) \;=\;\frac{1}{2}

    Exponentiate: . 2x \;=\;e^{\frac{1}{2}}

    Divide by 2: . \boxed{x \;=\;\frac{1}{2}e^{\frac{1}{2}}}

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