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I was given this problem in class:

$\frac{100}{e^{-2x}}=50$

I attempted to to solve it:

$100=50(e^{-2x})$

$e^{-2x}=2$

$\ln e^{-2x}= \ln2$

$-2x=\ln 2$

$x=-\frac {\ln2}{2}$

Would this be correct?

1 Answers 1

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Yes, this is correct! Well done!

Ultimately, you can rewrite this answer as $x = -ln(\sqrt{2})$ or $x = ln(\frac{\sqrt{2}}{2})$

  • 0
    Could you show me how I could get from $-\frac{\ln2}{2}$ to $-\ln(\sqrt{2})$? – 2017-02-14
  • 0
    Use the property: $a*ln(b) = ln(b^a)$ – 2017-02-14