4^3x-3=64 eching

$$4 ^ { 3 x - 3 } = 64$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{3x-3}=64$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{3x-3})=\log(64)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(3x-3\right)\log(4)=\log(64)$$

Ikki tarafini \log(4) ga bo‘ling.

$$3x-3=\frac{\log(64)}{\log(4)}$$

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

$$3x-3=\log_{4}\left(64\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$3x=3-\left(-3\right)$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{6}{3}$$

x uchun yechish (complex solution)

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

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