3^-1x-1=1/9 eching

$$3 ^ { - 1 x - 1 } = \frac { 1 } { 9 }$$

x uchun yechish

$$x=1$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{-x-1}=\frac{1}{9}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{-x-1})=\log(\frac{1}{9})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-x-1\right)\log(3)=\log(\frac{1}{9})$$

Ikki tarafini \log(3) ga bo‘ling.

$$-x-1=\frac{\log(\frac{1}{9})}{\log(3)}$$

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

$$-x-1=\log_{3}\left(\frac{1}{9}\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$-x=-2-\left(-1\right)$$

Ikki tarafini -1 ga bo‘ling.

$$x=-\frac{1}{-1}$$

x uchun yechish (complex solution)

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

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