3^4-x=2 eching

$$3 ^ { 4 - x } = 2$$

x uchun yechish

$$x=-\log_{3}\left(2\right)+4\approx 3,369070246$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{-x+4}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{-x+4})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-x+4\right)\log(3)=\log(2)$$

Ikki tarafini \log(3) ga bo‘ling.

$$-x+4=\frac{\log(2)}{\log(3)}$$

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

$$-x+4=\log_{3}\left(2\right)$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$-x=\log_{3}\left(2\right)-4$$

Ikki tarafini -1 ga bo‘ling.

$$x=\frac{\log_{3}\left(2\right)-4}{-1}$$

x uchun yechish (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(3)}-\log_{3}\left(2\right)+4$$

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