To solve the equation for x, first divide both sides of the equation by 4 to get [tex]e^{2.7x}=\frac{33}{4}[/tex]. Then, take the natural logarithm of both sides (base e) to get [tex]\ln e^{2.7x} = \ln (33/4)[/tex]. The left hand side of this equation if equal to 2.7x, so we get [tex]2.7x = \ln(33/4)[/tex]. The final step is to divide both sides of the equation by 2.7, to get that [tex]x =\frac{ \ln (33/4)}{2.7}[/tex]. This is approximately equal to 0.782.
