5^x-2=1 eching

$$5 ^ { x - 2 } = 1$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x-2}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x-2})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-2\right)\log(5)=\log(1)$$

Ikki tarafini \log(5) ga bo‘ling.

$$x-2=\frac{\log(1)}{\log(5)}$$

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

$$x-2=\log_{5}\left(1\right)$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=-\left(-2\right)$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(5)}+2$$

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