Datrys x=5^5x5^-y

$$x= { 5 }^{ 5 } x { 5 }^{ -y }$$

Datrys ar gyfer x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }y=\frac{2\pi n_{1}i}{\ln(5)}+5\end{matrix}\right.$$

Camau ar gyfer Datrys Hafaliad Llinol

Cyfrifo 5 i bŵer 5 a chael 3125.

$$x=3125x\times 5^{-y}$$

Tynnu 3125x\times 5^{-y} o'r ddwy ochr.

$$x-3125x\times 5^{-y}=0$$

Cyfuno pob term sy'n cynnwys x.

$$\left(1-3125\times 5^{-y}\right)x=0$$

Mae'r hafaliad yn y ffurf safonol.

$$\left(-\frac{3125}{5^{y}}+1\right)x=0$$

Rhannwch 0 â 1-3125\times 5^{-y}.

$$x=0$$

Datrys ar gyfer x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=5\end{matrix}\right.$$

Camau ar gyfer Datrys Hafaliad Llinol

Cyfrifo 5 i bŵer 5 a chael 3125.

$$x=3125x\times 5^{-y}$$

Tynnu 3125x\times 5^{-y} o'r ddwy ochr.

$$x-3125x\times 5^{-y}=0$$

Cyfuno pob term sy'n cynnwys x.

$$\left(1-3125\times 5^{-y}\right)x=0$$

Mae'r hafaliad yn y ffurf safonol.

$$\left(-\frac{3125}{5^{y}}+1\right)x=0$$

Rhannwch 0 â 1-3125\times 5^{-y}.

$$x=0$$

Datrys ar gyfer y

$$\left\{\begin{matrix}\\y=5\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfrifo 5 i bŵer 5 a chael 3125.

$$x=3125x\times 5^{-y}$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$3125x\times 5^{-y}=x$$

Rhannu’r ddwy ochr â 3125x.

$$5^{-y}=\frac{1}{3125}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{-y})=\log(\frac{1}{3125})$$

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

$$-y\log(5)=\log(\frac{1}{3125})$$

Rhannu’r ddwy ochr â \log(5).

$$-y=\frac{\log(\frac{1}{3125})}{\log(5)}$$

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

$$-y=\log_{5}\left(\frac{1}{3125}\right)$$

Rhannu’r ddwy ochr â -1.

$$y=-\frac{5}{-1}$$

Datrys ar gyfer y (complex solution)

$$\left\{\begin{matrix}\\y=-\frac{2\pi n_{1}i}{\ln(5)}+5\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$