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Math Help - If my equation is a^b=c, how do I get b by itself?

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    If my equation is a^b=c, how do I get b by itself?

    Thank you!
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    Re: If my equation is a^b=c, how do I get b by itself?

    i believe you'd use logarithms
    Working with Exponents and Logarithms
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    Re: If my equation is a^b=c, how do I get b by itself?

    I have been using natural logs. I've been using the equation f(x) = a*e^bx but I'm not sure if that is even the right equation or if I've been doing the work correctly.
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    Re: If my equation is a^b=c, how do I get b by itself?

    a^b=c implies \log_a(c)=b.
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    Re: If my equation is a^b=c, how do I get b by itself?

    Quote Originally Posted by Dima110 View Post
    Thank you!
    Method 1: Use a logarithm of base a.

    \displaystyle \begin{align*} a^b &= c \\ \log_a{\left( a^b \right)} &= \log_a{(c)} \\ b &= \log_a{(c)} \end{align*}

    Method 2: Use a logarithm of ANY base.

    \displaystyle \begin{align*} a^b &= c \\ \log_k{\left( a^b \right)} &= \log_k{\left( c \right)} \\ b \log_k{(a)} &= \log_k{(c)} \\ b &= \frac{\log_k{(c)}}{\log_k{(a)}}  \end{align*}
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