Issolvi y*1032^x=2y

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

Solvi għal y (complex solution)

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Naqqas 2y miż-żewġ naħat.

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

Ikkombina t-termini kollha li fihom y.

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

Iddividi 0 b'1032^{x}-2.

$$y=0$$

Solvi għal x

$$\left\{\begin{matrix}\\x=\log_{1032}\left(2\right)\approx 0.099887853\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Passi għall-Użu ta' Definizzjoni ta' Logaritmu

Uża r-regoli tal-esponenti u l-logaritmi biex issolvi l-ekwazzjoni.

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

Iddividi ż-żewġ naħat b'y.

$$1032^{x}=2$$

Ħu l-logaritmu taż-żewġ naħat tal-ekwazzjoni.

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

Il-logaritmu ta ' numru imqajjem għall-enerġija hi l-qawwa ħinijiet Il-logaritmu tal-għadd.

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

Iddividi ż-żewġ naħat b'\log(1032).

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

Bil-formula bidla tal-bażi \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

Solvi għal y

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Naqqas 2y miż-żewġ naħat.

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

Ikkombina t-termini kollha li fihom y.

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

Iddividi 0 b'1032^{x}-2.

$$y=0$$

Solvi għal x (complex solution)

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