Solve for a
a=\frac{1}{e^{x}}
Solve for x (complex solution)
x=-\ln(a)+2\pi n_{1}i
n_{1}\in \mathrm{Z}
a\neq 0
Solve for x
x=-\ln(a)
a>0
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ae^{x}-1=0
Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.
ae^{x}=1
Add 1 to both sides. Anything plus zero gives itself.
e^{x}a=1
The equation is in standard form.
\frac{e^{x}a}{e^{x}}=\frac{1}{e^{x}}
Divide both sides by e^{x}.
a=\frac{1}{e^{x}}
Dividing by e^{x} undoes the multiplication by e^{x}.
a=\frac{1}{e^{x}}\text{, }a\neq 0
Variable a cannot be equal to 0.
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