Leysa y=ae^kx

$$y = a e ^ { k x }$$

Leystu fyrir a

$$a=\frac{y}{e^{kx}}$$

Skref til að leysa línulega jöfnu

Skipta um hliðar svo allir liðir breytunnar séu vinstra megin.

$$ae^{kx}=y$$

Jafnan er í staðalformi.

$$e^{kx}a=y$$

Deildu báðum hliðum með e^{kx}.

$$\frac{e^{kx}a}{e^{kx}}=\frac{y}{e^{kx}}$$

Að deila með e^{kx} afturkallar margföldun með e^{kx}.

$$a=\frac{y}{e^{kx}}$$

Leystu fyrir k (complex solution)

$$\left\{\begin{matrix}k=\frac{2\pi n_{1}i}{x}+\frac{\ln(\frac{y}{a})}{x}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 0\text{ and }a\neq 0\text{ and }y\neq 0\\k\in \mathrm{C}\text{, }&\left(y=0\text{ and }a=0\right)\text{ or }\left(a=y\text{ and }x=0\text{ and }y\neq 0\right)\end{matrix}\right.$$

Leystu fyrir k

$$\left\{\begin{matrix}k=\frac{\ln(\frac{y}{a})}{x}\text{, }&\left(x\neq 0\text{ and }y>0\text{ and }a>0\right)\text{ or }\left(x\neq 0\text{ and }y<0\text{ and }a<0\right)\\k\in \mathrm{R}\text{, }&\left(y=0\text{ and }a=0\right)\text{ or }\left(a=y\text{ and }x=0\text{ and }y\neq 0\right)\end{matrix}\right.$$