4^4x+4=9 eching

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

x uchun yechish

$$x=\frac{\log_{2}\left(3\right)-4}{4}\approx -0,603759375$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

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

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(4x+4\right)\log(4)=\log(9)$$

Ikki tarafini \log(4) ga bo‘ling.

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

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

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

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$4x=\log_{2}\left(3\right)-4$$

Ikki tarafini 4 ga bo‘ling.

$$x=\frac{\log_{2}\left(3\right)-4}{4}$$