9^x-4=81 eching

$$9 ^ { x - 4 } = 81$$

x uchun yechish

$$x=6$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9^{x-4}=81$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{x-4})=\log(81)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-4\right)\log(9)=\log(81)$$

Ikki tarafini \log(9) ga bo‘ling.

$$x-4=\frac{\log(81)}{\log(9)}$$

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

$$x-4=\log_{9}\left(81\right)$$

4 ni tenglamaning ikkala tarafiga qo'shish.

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

x uchun yechish (complex solution)

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

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