3^2x-3=9 eching

$$3 ^ { 2 x - 3 } = 9$$

x uchun yechish

$$x = \frac{5}{2} = 2\frac{1}{2} = 2,5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{2x-3}=9$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{2x-3})=\log(9)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x-3\right)\log(3)=\log(9)$$

Ikki tarafini \log(3) ga bo‘ling.

$$2x-3=\frac{\log(9)}{\log(3)}$$

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

$$2x-3=\log_{3}\left(9\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

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

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{5}{2}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(3)}+\frac{5}{2}$$

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