2^x=4 eching

$$2 ^ { x } = 4$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{x}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(2) ga bo‘ling.

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

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

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

x uchun yechish (complex solution)

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

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