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

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

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

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

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

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

$x = \dfrac{\ln(3)}{\ln(5)-\ln(3)} = \dfrac{\ln(3)}{\ln\left(\frac 5 3\right)}$

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

Thank you! I understand now

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

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

$\displaystyle 5^x=3^x*3^1$

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

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

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

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

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