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Math Help - Exponential & Logarithmic Equations

  1. #1
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    Exponential & Logarithmic Equations

    4^(x+2)=6^(-2x-3)
    I am completely clueless how to do this problem because neither my teacher nor my book explained it very well. Please HELP
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  2. #2
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    Re: Exponential & Logarithmic Equations

    Make use of one of the rules of logs, \log a^{k} = k\log a.
    It doesn't matter what base you choose, the rule works for any base.
    Take logs of your equation, apply the rule and then solve for x.
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  3. #3
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    Re: Exponential & Logarithmic Equations

    Quote Originally Posted by paigesisco View Post
    4^(x+2)=6^(-2x-3)
    I am completely clueless how to do this problem because neither my teacher nor my book explained it very well.

    Write it as 2^{2x+4}=(2^{-2x-3})(3^{-2x-3})
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    Re: Exponential & Logarithmic Equations

    Another way to do it,

    Remember that

    6= 4^{log_4 {6}}

    So we have

    4^{x+2}=4^{(log_4 {6})\cdot(-2x-3)}

    then

    x+2= (log_4 {6})\cdot(-2x-3)
    Thanks from ReneG
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