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Math Help - Solve exponential equations?

  1. #1
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    Solve exponential equations?

    Hey I was wondering if you could help me find the answer to some practice questions we were given. I have a quiz tomorrow morning but I'm not even sure if I'm doing it right. Whats the point of practice questions if I don't even have the answers

    I'm asked to solve exponential equations here are two of the more difficult ones I'm not sure how to do:

    Solve exponential equations?-equations.png

    Could really use a small explanation, or just the steps alone so I can interpret it myself
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    Re: ....

    sorry about the double
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  3. #3
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    Re: ....

    Quote Originally Posted by needhelp96 View Post
    Hey I was wondering if you could help me find the answer to some practice questions we were given. I have a quiz tomorrow morning but I'm not even sure if I'm doing it right. Whats the point of practice questions if I don't even have the answers

    I'm asked to solve exponential equations here are two of the more difficult ones I'm not sure how to do:

    Click image for larger version. 

Name:	equations.png 
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    Could really use a small explanation, or just the steps alone so I can interpret it myself
    $2^{x+3}-2^x=224$

    $2^x\cdot 2^3 - 2^x = 224$

    $2^x\left(2^3-1\right)=224$

    Spoiler:
    $2^x\left(8-1\right)=224$

    $2^x(7)=224$

    $2^x=32$

    $x=5$


    $4\left(2^{2x}\right)+31\left(2^x\right)-8=0$

    $4\left(2^x\right)^2 + 31\left(2^x\right)-8=0$

    let $u=2^x$

    $4u^2+31u-8=0$

    $(8+u)(4u-1)=0$

    $u=\{-8, \frac{1}{4}\}$

    as $u=2^x>0, u=-8\mbox{ can be disregarded.}$

    $2^x=\frac{1}{4}$

    $x=-2$
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