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Math Help - Logarithmic equation is equivalent to exponential equations

  1. #1
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    Logarithmic equation is equivalent to exponential equations

    Hello,

    I was wondering how to change a logarithmic equation to a exponential equation.
    For example: 9x = log6​ d
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  2. #2
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    Re: Logarithmic equation is equivalent to exponential equations

    Quote Originally Posted by IStandAlone99 View Post
    Hello,

    I was wondering how to change a logarithmic equation to a exponential equation.
    For example: 9x = log6​ d
    in this case, since the logarithm is base 6, you would get

    $$9x=\log_6(d) \Rightarrow 6^{9x}=d$$

    alternatively you could convert to natural logs

    $$9x=\frac{\ln(d)}{\ln(6)}$$

    $$\Large e^{9x}=e^{\frac{\ln(d)}{\ln(6)}}=d^{\frac{1}{\ln(6 )}}$$
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    Re: Logarithmic equation is equivalent to exponential equations

    Quote Originally Posted by IStandAlone99 View Post
    Hello,

    I was wondering how to change a logarithmic equation to a exponential equation.
    For example: 9x = log6​ d
    Here is the general rule

    $Given\ b,\ c > 0\ and\ b \ne 1: a = log_b(c) \iff c = b^a.$ This is a definition and needs to be memorized.

    So, as Romsek has already explained, $9x = log_6(d) \implies d = 6^{9x}.$

    The only tricky thing is that sometimes the base of the logarithm is implied.
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