4^x-16=0 eching

$${ 4 }^{ x } -16=0$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{x}-16=0$$

16 ni tenglamaning ikkala tarafiga qo'shish.

$$4^{x}=16$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{x})=\log(16)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(4)=\log(16)$$

Ikki tarafini \log(4) ga bo‘ling.

$$x=\frac{\log(16)}{\log(4)}$$

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

$$x=\log_{4}\left(16\right)$$

x uchun yechish (complex solution)

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

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