22(1/3)^x-7=22 eching

$$22 ( 1 / 3 ) ^ { x - 7 } = 22$$

x uchun yechish

$$x=7$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$22\times \left(\frac{1}{3}\right)^{x-7}=22$$

Ikki tarafini 22 ga bo‘ling.

$$\left(\frac{1}{3}\right)^{x-7}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{1}{3}\right)^{x-7})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-7\right)\log(\frac{1}{3})=\log(1)$$

Ikki tarafini \log(\frac{1}{3}) ga bo‘ling.

$$x-7=\frac{\log(1)}{\log(\frac{1}{3})}$$

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

$$x-7=\log_{\frac{1}{3}}\left(1\right)$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$x=-\left(-7\right)$$

x uchun yechish (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(3)}+7$$

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