Solve the exponential equation e^(2x)+2e^(-y)=c

 Exercise

$e^{2x}+2e^{-y}=c$

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We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $e^{2x}$ from both sides of the equation

$2e^{-y}=c-e^{2x}$

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Divide both sides of the equation by $2$

$e^{-y}=\frac{c-e^{2x}}{2}$

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We can take out the unknown from the exponent by applying natural logarithm to both sides of the equation

$\ln\left(e^{-y}\right)=\ln\left(\frac{c-e^{2x}}{2}\right)$

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Apply the formula: $\ln\left(e^x\right)$$=x$, where $x=-y$

$-y=\ln\left(\frac{c-e^{2x}}{2}\right)$

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Multiply both sides of the equation by $-1$

$y=-\ln\left(\frac{c-e^{2x}}{2}\right)$

$y=-\ln\left(\frac{c-e^{2x}}{2}\right)$

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