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

$$ x = e^{1+ \ln(5)} = e^{1+5} = e^6$$

What exactly am I doing wrong here?

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    $\begingroup$ it is $e\cdot 5$ not $e^{1+5}$ $\endgroup$
    – user31280
    Commented Jan 21, 2013 at 20:34
  • $\begingroup$ Also $5\ne\ln(5)$ $\endgroup$ Commented Aug 17, 2023 at 12:04

2 Answers 2

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You change $\ln(5)$ to $5$ in the exponent, when it should be $$e^{1+\ln(5)}=e\cdot e^{\ln(5)}=5e.$$

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  • $\begingroup$ Thank you, can't believe I missed that. $\endgroup$ Commented Jan 21, 2013 at 20:36
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    $\begingroup$ @ZafarS: You're welcome; we all make mistakes at some point. $\endgroup$
    – Clayton
    Commented Jan 21, 2013 at 20:37
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$$ \ln x = 1 + \ln 5$$ $$ \ln x = \ln e + \ln 5$$ $$\ln x=\ln(5e)$$ $$x=5e$$

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