3^x+2=81 eching

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

x uchun yechish

$$x=2$$

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).

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=4-2$$

x uchun yechish (complex solution)

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

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