Datrys y*1032^x=2y

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

Datrys ar gyfer y (complex solution)

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

Camau ar gyfer Datrys Hafaliad Llinol

Tynnu 2y o'r ddwy ochr.

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

Cyfuno pob term sy'n cynnwys y.

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

Rhannwch 0 â 1032^{x}-2.

$$y=0$$

Datrys ar gyfer x

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

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

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

Rhannu’r ddwy ochr â y.

$$1032^{x}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

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

Logarithm rhif wedi’i godi i bŵer yw’r pŵer wedi’i lluosi â logarithm y rhif.

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

Rhannu’r ddwy ochr â \log(1032).

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

Gyda’r fformiwla newid-sail \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

Datrys ar gyfer y

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

Camau ar gyfer Datrys Hafaliad Llinol

Tynnu 2y o'r ddwy ochr.

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

Cyfuno pob term sy'n cynnwys y.

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

Rhannwch 0 â 1032^{x}-2.

$$y=0$$

Datrys ar gyfer x (complex solution)

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