Riješi y*1032^x=2y

$$y \times { 1032 }^{ x } =2y$$

Riješite za y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{2\pi n_{1}i}{\ln(1032)}+\log_{1032}\left(2\right)\end{matrix}\right,$$

Koraci za rješavanje linearne jednačine

Oduzmite 2y s obje strane.

$$y\times 1032^{x}-2y=0$$

Kombinirajte sve termine koji sadrže y.

$$\left(1032^{x}-2\right)y=0$$

Podijelite 0 sa 1032^{x}-2.

$$y=0$$

Riješite za x

$$\left\{\begin{matrix}\\x=\log_{1032}\left(2\right)\approx 0,099887853\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right,$$

Koraci pomoću definicije logaritma

Koristite pravila eksponenata i logaritama za rješavanje jednačine.

$$y\times 1032^{x}=2y$$

Podijelite obje strane s y.

$$1032^{x}=2$$

Izračunajte logaritam obje strane jednačine.

$$\log(1032^{x})=\log(2)$$

Logaritam broja podignutog na stepen je stepen puta logaritam broja.

$$x\log(1032)=\log(2)$$

Podijelite obje strane s \log(1032).

$$x=\frac{\log(2)}{\log(1032)}$$

Po formuli promjene osnove \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{1032}\left(2\right)$$

Riješite za y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=\log_{1032}\left(2\right)\end{matrix}\right,$$

Koraci za rješavanje linearne jednačine

Oduzmite 2y s obje strane.

$$y\times 1032^{x}-2y=0$$

Kombinirajte sve termine koji sadrže y.

$$\left(1032^{x}-2\right)y=0$$

Podijelite 0 sa 1032^{x}-2.

$$y=0$$

Riješite za x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{2\pi n_{1}i}{\ln(1032)}+\log_{1032}\left(2\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right,$$