3^x-2=81 eching

$$3 ^ { x - 2 } = 81$$

x uchun yechish

$$x=6$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{x-2}=81$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x-2})=\log(81)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-2\right)\log(3)=\log(81)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x-2=\frac{\log(81)}{\log(3)}$$

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

$$x-2=\log_{3}\left(81\right)$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4-\left(-2\right)$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+6$$

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