9^2x+2=27 eching

$$9 ^ { 2 x + 2 } = 27$$

x uchun yechish

$$x=-\frac{1}{4}=-0,25$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9^{2x+2}=27$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{2x+2})=\log(27)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x+2\right)\log(9)=\log(27)$$

Ikki tarafini \log(9) ga bo‘ling.

$$2x+2=\frac{\log(27)}{\log(9)}$$

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

$$2x+2=\log_{9}\left(27\right)$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$2x=\frac{3}{2}-2$$

Ikki tarafini 2 ga bo‘ling.

$$x=-\frac{\frac{1}{2}}{2}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{2\ln(3)}-\frac{1}{4}$$

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