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Laws of logs question 
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#1
Apr2312, 08:25 PM

P: 90

I'm reading about how the chemistry kinetics equations are derived and heres something I don't get. How does this:
get turned into this: [itex][A] = [A]_{0}*e^{kt}[/itex]? When I try to derive it, I first get this: [itex]ln[A]  ln[A]_{0} = kt[/itex]. Then I isolate ln[A] and get: [itex]ln[A] = ln[A]_{0}  kt[/itex] then I reverse the ln on both sides of the equation and get: [itex][A] = [A]_{0}  e^{kt}[/itex]. I don't understand how the two terms end up multiplied rather than subtracted. 


#2
Apr2312, 08:32 PM

P: 26

By reverse you use e as a index for exponentiation, so lets say : ln a = ln b  c e^(ln a) = e^(ln b  c) u got your exponentialtion wrong. 


#3
Apr2312, 09:30 PM

P: 392

## \begin{eqnarray*} \displaystyle ln\frac{[A]}{[A]_0} &=& kt\\ \displaystyle e^{ln\frac{[A]}{[A]_0}}&=& e^{kt}\\ \displaystyle \frac{[A]}{[A]_0} &=& e^{kt}\\ \displaystyle [A] &=& [A]_0 e^{kt}\\ \end{eqnarray*} ## 


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