Analytical methods involve solving equations using algebraic techniques. These methods are particularly useful for equations that can be manipulated into standard forms.
Consider the equation $e^{2x} - 5e^x + 4 = 0$. This can be solved analytically by substituting $y = e^x$:
Thus, the solutions are $x = \ln 4$ and $x = 0$.
When solving exponential equations analytically, try to isolate the exponential term and then use logarithms to solve for the variable.
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