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Go Yankees! asked in Science & MathematicsMathematics · 8 years ago

Please solve e^4x = 5e^2x?

I have no clue how to solve this problem and neither does my roommate, please help!

4 Answers

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  • ?
    Lv 7
    8 years ago

    e^4x = 5e^2x

    take the log of both sides

    ln e^4x = 4x

    ln 5e^2x = ln 5 + ln e^2x = ln 5 + 2x

    4x = ln 5 + 2x

    2x = ln 5

    x = 1/2 ln 5

  • dennis
    Lv 6
    8 years ago

    Let e^2x = y then we have y^2 = 5y and so y = 0 or 5.Now e^2x = 0 is impossible and so all we have is e^2x = 5 and so 2x = ln(5) so that x = (ln5)/2.

  • ?
    Lv 7
    8 years ago

    e^4x = 5e^2x

    is equivalent to :

    e^(4x - 2x) = 5

    Ln(e^(2x) ) = Ln5

    2x = Ln5

    x = (Ln5) / 2

    hope it' ll help !!

  • ?
    Lv 4
    8 years ago

    e^(4x) = 5e^(2x)

    lne^(4x)=ln5e^(2x)

    4x=ln5+2x

    2x=ln5

    x=(ln5)/2

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