3(6)^2x-3=648 eching

$$3 ( 6 ) ^ { 2 x - 3 } = 648$$

x uchun yechish

$$x=3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3\times 6^{2x-3}=648$$

Ikki tarafini 3 ga bo‘ling.

$$6^{2x-3}=216$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(6^{2x-3})=\log(216)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x-3\right)\log(6)=\log(216)$$

Ikki tarafini \log(6) ga bo‘ling.

$$2x-3=\frac{\log(216)}{\log(6)}$$

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

$$2x-3=\log_{6}\left(216\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$2x=3-\left(-3\right)$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{6}{2}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(6)}+3$$

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