2(1/3)^x+1=8 eching

$$2 ( \frac { 1 } { 3 } ) ^ { x + 1 } = 8$$

x uchun yechish

$$x=-2\log_{3}\left(2\right)-1\approx -2,261859507$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2\times \left(\frac{1}{3}\right)^{x+1}=8$$

Ikki tarafini 2 ga bo‘ling.

$$\left(\frac{1}{3}\right)^{x+1}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{1}{3}\right)^{x+1})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(\frac{1}{3})=\log(4)$$

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

$$x+1=\frac{\log(4)}{\log(\frac{1}{3})}$$

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

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

Tenglamaning ikkala tarafidan 1 ni ayirish.

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

x uchun yechish (complex solution)

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

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