y*1032^x=2y eching

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

y uchun yechish (complex solution)

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 2y ni ayirish.

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

y'ga ega bo'lgan barcha shartlarni birlashtirish.

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

0 ni 1032^{x}-2 ga bo'lish.

$$y=0$$

x uchun yechish

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

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

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

Ikki tarafini y ga bo‘ling.

$$1032^{x}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(1032) ga bo‘ling.

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

Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

y uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 2y ni ayirish.

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

y'ga ega bo'lgan barcha shartlarni birlashtirish.

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

0 ni 1032^{x}-2 ga bo'lish.

$$y=0$$

x uchun yechish (complex solution)

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