Solve for C
C=\frac{y}{e^{x}}
Solve for x (complex solution)
\left\{\begin{matrix}x=2\pi n_{1}i+\ln(\frac{y}{C})\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq 0\text{ and }C\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }C=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\ln(\frac{y}{C})\text{, }&\left(y<0\text{ and }C<0\right)\text{ or }\left(y>0\text{ and }C>0\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }C=0\end{matrix}\right.
Graph
Share
Copied to clipboard
Ce^{x}=y
Swap sides so that all variable terms are on the left hand side.
e^{x}C=y
The equation is in standard form.
\frac{e^{x}C}{e^{x}}=\frac{y}{e^{x}}
Divide both sides by e^{x}.
C=\frac{y}{e^{x}}
Dividing by e^{x} undoes the multiplication by e^{x}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}