Vyriešiť y=hx^k

$$y = h x ^ { k }$$

Riešenie pre h (complex solution)

$$\left\{\begin{matrix}h=\frac{y}{x^{k}}\text{, }&k=0\text{ or }x\neq 0\\h\in \mathrm{C}\text{, }&y=0\text{ and }x=0\text{ and }k\neq 0\end{matrix}\right,$$

Postup riešenia lineárnej rovnice

Prehoďte strany tak, aby všetky premenné stáli na ľavej strane.

$$hx^{k}=y$$

Rovnica je v štandardnom formáte.

$$x^{k}h=y$$

Vydeľte obe strany hodnotou x^{k}.

$$\frac{x^{k}h}{x^{k}}=\frac{y}{x^{k}}$$

Delenie číslom x^{k} ruší násobenie číslom x^{k}.

$$h=\frac{y}{x^{k}}$$

Riešenie pre h

$$\left\{\begin{matrix}h=\frac{y}{x^{k}}\text{, }&x>0\text{ or }\left(Denominator(k)\text{bmod}2=1\text{ and }x<0\right)\\h\in \mathrm{R}\text{, }&y=0\text{ and }x=0\text{ and }k>0\end{matrix}\right,$$

Postup riešenia lineárnej rovnice

Prehoďte strany tak, aby všetky premenné stáli na ľavej strane.

$$hx^{k}=y$$

Rovnica je v štandardnom formáte.

$$x^{k}h=y$$

Vydeľte obe strany hodnotou x^{k}.

$$\frac{x^{k}h}{x^{k}}=\frac{y}{x^{k}}$$

Delenie číslom x^{k} ruší násobenie číslom x^{k}.

$$h=\frac{y}{x^{k}}$$

Riešenie pre k (complex solution)

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

Riešenie pre k

$$\left\{\begin{matrix}k=\log_{x}\left(\frac{y}{h}\right)\text{, }&\left(y<0\text{ and }h<0\text{ and }x\neq 1\text{ and }x>0\right)\text{ or }\left(y>0\text{ and }h>0\text{ and }x\neq 1\text{ and }x>0\right)\\k\in \mathrm{R}\text{, }&\left(y=0\text{ and }h=0\text{ and }x>0\right)\text{ or }\left(y=0\text{ and }h=0\text{ and }x<0\text{ and }Denominator(k)\text{bmod}2=1\right)\text{ or }\left(y=h\text{ and }h\neq 0\text{ and }x=1\right)\text{ or }\left(y=-h\text{ and }Denominator(k)\text{bmod}2=1\text{ and }Numerator(k)\text{bmod}2=1\text{ and }h\neq 0\text{ and }x=-1\right)\\k>0\text{, }&x=0\text{ and }y=0\end{matrix}\right,$$