3^2x=81 eching

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

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

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

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(3)=\log(81)$$

Ikki tarafini \log(3) ga bo‘ling.

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

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

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

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{4}{2}$$

x uchun yechish (complex solution)

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

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