2^x+1=4 eching

$$2 ^ { x + 1 } = 4$$

x uchun yechish

$$x=1$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{x+1}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x+1})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(2)=\log(4)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x+1=\frac{\log(4)}{\log(2)}$$

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

$$x+1=\log_{2}\left(4\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=2-1$$

x uchun yechish (complex solution)

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

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