9^3-x=81 eching

$$9 ^ { 3 - x } = 81$$

x uchun yechish

$$x=1$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9^{-x+3}=81$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{-x+3})=\log(81)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-x+3\right)\log(9)=\log(81)$$

Ikki tarafini \log(9) ga bo‘ling.

$$-x+3=\frac{\log(81)}{\log(9)}$$

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

$$-x+3=\log_{9}\left(81\right)$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$-x=2-3$$

Ikki tarafini -1 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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