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solve (С*(((2.7^-(t/(R*C)))-G)^2))/2=A for t

 Aug 28, 2016
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solve (С*(((2.7^-(t/(R*C)))-G)^2))/2=A for t

 

\(\begin{align}(С*([(2.7^{-(t/(R*C))})-G]^2))/2&=A\\~\\ \frac{С\;[(2.7^{-(t/(R*C))})-G]^2}{2}&=A\\~\\ \;[(2.7^{-(t/(R*C))})-G]^2&=\frac{2A}{C}\\~\\ (2.7^{-(t/(R*C))})-G&=\pm\sqrt{\frac{2A}{C}}\\~\\ 2.7^{-(t/(R*C))}&=G\pm\sqrt{\frac{2A}{C}}\\~\\ log[2.7^{-(t/(R*C))}]&=log\left[G\pm\sqrt{\frac{2A}{C}}\;\right]\\~\\ -(t/(R*C))log[2.7]&=log\left[G\pm\sqrt{\frac{2A}{C}}\;\right]\\~\\ t/(RC)&=\frac{-log\left[G\pm\sqrt{\frac{2A}{C}}\;\right]}{log(2.7)}\\~\\ t&=\frac{-RClog\left[G\pm\sqrt{\frac{2A}{C}}\;\right]}{log(2.7)}\\~\\ \end{align}\)

 Aug 28, 2016

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