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Math Help - Exponential Equation

  1. #1
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    Exponential Equation

    How to solve:
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  2. #2
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    Hello, thebristolsound!

    Solve: . e^{2x} + 3e^x - 10 \:=\:0

    Factor: . (e^x + 5)(e^x - 2) \:=\:0

    Set each factor equal to zero and solve.

    . . e^x + 5 \:=\:0 \quad\Rightarrow\quad e^x \:=\:-5 . . . no real roots

    . . e^x - 2 \:=\:0 \quad\Rightarrow\quad e^x \:=\:2 \quad\Rightarrow\quad\boxed{ x \:=\:\ln 2}

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  3. #3
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    Smile

    hello
    u can also put e^{x}=u and solve for u,
    u^2+3u-10=0
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  4. #4
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    Following on from Soroban you can also have complex roots:

    <br />
(e^x + 5)(e^x - 2) \:=\:0<br />

    <br />
e^x = - 5<br />

    x = ln(5)+ i\pi
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