2=3^x+1 eching

$$2= { 3 }^{ x+1 }$$

x uchun yechish

$$x=\log_{3}\left(2\right)-1\approx -0,369070246$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3^{x+1}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(3)=\log(2)$$

Ikki tarafini \log(3) ga bo‘ling.

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

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

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

Tenglamaning ikkala tarafidan 1 ni ayirish.

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

x uchun yechish (complex solution)

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

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