(2^2)^x=64 eching

$$( 2 ^ { 2 } ) ^ { x } = 64$$

x uchun yechish

$$x=3$$

Logaritm ifodasidan foydalanish qadamlari

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$4^{x}=64$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{x})=\log(64)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(4)=\log(64)$$

Ikki tarafini \log(4) ga bo‘ling.

$$x=\frac{\log(64)}{\log(4)}$$

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

$$x=\log_{4}\left(64\right)$$

x uchun yechish (complex solution)

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

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