9^x-1=27 eching

$$9 ^ { x - 1 } = 27$$

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.

$$9^{x-1}=27$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{x-1})=\log(27)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-1\right)\log(9)=\log(27)$$

Ikki tarafini \log(9) ga bo‘ling.

$$x-1=\frac{\log(27)}{\log(9)}$$

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

$$x-1=\log_{9}\left(27\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3}{2}-\left(-1\right)$$

x uchun yechish (complex solution)

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

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