9^2x=4 eching

$$9 ^ { 2 x } = 4$$

x uchun yechish

$$x=\frac{\log_{3}\left(2\right)}{2}\approx 0,315464877$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9^{2x}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{2x})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(9)=\log(4)$$

Ikki tarafini \log(9) ga bo‘ling.

$$2x=\frac{\log(4)}{\log(9)}$$

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

$$2x=\log_{9}\left(4\right)$$

Ikki tarafini 2 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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