Réitigh y*1.032^x=2y

$$y \times { 1.032 }^{ x } =2y$$

Réitigh do y. (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{2\pi n_{1}i}{\ln(\frac{129}{125})}+\frac{\ln(2)}{\ln(\frac{129}{125})}\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain 2y ón dá thaobh.

$$y\times 1.032^{x}-2y=0$$

Comhcheangail na téarmaí ar fad ina bhfuil y.

$$\left(1.032^{x}-2\right)y=0$$

Roinn 0 faoi 1.032^{x}-2.

$$y=0$$

Réitigh do x.

$$\left\{\begin{matrix}\\x=\log_{1.032}\left(2\right)\approx 22.005603579\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Úsáid rialacha na n-easpónant agus na logartam chun an chothromóid a réiteach.

$$y\times 1.032^{x}=2y$$

Roinn an dá thaobh faoi y.

$$1.032^{x}=2$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1.032^{x})=\log(2)$$

Is ionann logartam uimhreacha a ardaítear go cumhacht agus an chumhacht méadaithe faoi logartam na huimhreach.

$$x\log(1.032)=\log(2)$$

Roinn an dá thaobh faoi \log(1.032).

$$x=\frac{\log(2)}{\log(1.032)}$$

Leis an bhfoirmle athrú boinn \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{1.032}\left(2\right)$$

Réitigh do y.

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=\frac{\ln(2)}{\ln(\frac{129}{125})}\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain 2y ón dá thaobh.

$$y\times 1.032^{x}-2y=0$$

Comhcheangail na téarmaí ar fad ina bhfuil y.

$$\left(1.032^{x}-2\right)y=0$$

Roinn 0 faoi 1.032^{x}-2.

$$y=0$$

Réitigh do x. (complex solution)

$$\left\{\begin{matrix}\\x=\frac{i\times 2\pi n_{1}}{\ln(1.032)}+\log_{1.032}\left(2\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$