2017^x-y=1 eching

$${ 2017 }^{ x-y } =1$$

x uchun yechish

$$x=y$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2017^{x-y}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2017^{x-y})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-y\right)\log(2017)=\log(1)$$

Ikki tarafini \log(2017) ga bo‘ling.

$$x-y=\frac{\log(1)}{\log(2017)}$$

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

$$x-y=\log_{2017}\left(1\right)$$

Tenglamaning ikkala tarafidan -y ni ayirish.

$$x=-\left(-y\right)$$

y uchun yechish

$$y=x$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2017^{-y+x}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2017^{-y+x})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-y+x\right)\log(2017)=\log(1)$$

Ikki tarafini \log(2017) ga bo‘ling.

$$-y+x=\frac{\log(1)}{\log(2017)}$$

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

$$-y+x=\log_{2017}\left(1\right)$$

Tenglamaning ikkala tarafidan x ni ayirish.

$$-y=-x$$

Ikki tarafini -1 ga bo‘ling.

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

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2017)}+y$$

$$n_{1}\in \mathrm{Z}$$

y uchun yechish (complex solution)

$$y=-\frac{2\pi n_{1}i}{\ln(2017)}+x$$

$$n_{1}\in \mathrm{Z}$$