4^x-3225=14 eching

$${ 4 }^{ x } -3225=14$$

x uchun yechish

$$x = \frac{\log_{2} {(3239)}}{2} \approx 5,830666376$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{x}-3225=14$$

3225 ni tenglamaning ikkala tarafiga qo'shish.

$$4^{x}=3239$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{x})=\log(3239)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(4)=\log(3239)$$

Ikki tarafini \log(4) ga bo‘ling.

$$x=\frac{\log(3239)}{\log(4)}$$

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

$$x=\log_{4}\left(3239\right)$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(3239\right)}{2}$$

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