2^x+1=128 eching

$$2 ^ { x + 1 } = 128$$

x uchun yechish

$$x=6$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{x+1}=128$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x+1})=\log(128)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(2)=\log(128)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x+1=\frac{\log(128)}{\log(2)}$$

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

$$x+1=\log_{2}\left(128\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=7-1$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+6$$

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