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Thread: How do I solve this exponential/logarithmic equation?

  1. #1
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    How do I solve this exponential/logarithmic equation?

    5^x = 3^(x+1)
    Sorry, I typed this on my phone, if its unclear: the 'x' and 'x + 1' are all in superscript.
    Any help would be greatly appreciated!

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  2. #2
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    Re: How do I solve this exponential/logarithmic equation?

    $5^x = 3^{x+1}$

    $e^{\ln(5)x} = e^{\ln(3)(x+1)}$

    $\ln(5) x = \ln(3) (x+1)$

    $(\ln(5) - \ln(3))x = \ln(3)$

    $x = \dfrac{\ln(3)}{\ln(5)-\ln(3)} = \dfrac{\ln(3)}{\ln\left(\frac 5 3\right)}$
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  3. #3
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    Re: How do I solve this exponential/logarithmic equation?

    Thank you! I understand now

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  4. #4
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    Re: How do I solve this exponential/logarithmic equation?

    An alternative way:
    5^x = 3^{(x+1)}

    5^x=3^x*3^1

    \frac{5^x}{3^x} =3

     (\frac{5}{3})^x =3

    \ln((\frac{5}{3})^x) =\ln 3

    x*\ln(\frac{5}{3}) =\ln 3

     x=\frac{\ln(3)}{\ln(\frac{5}{3})}
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