2^x+7=21 eching

$$2 ^ { x + 7 } = 21$$

x uchun yechish

$$x=\log_{2}\left(21\right)-7\approx -2,607682577$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{x+7}=21$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x+7})=\log(21)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+7\right)\log(2)=\log(21)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x+7=\frac{\log(21)}{\log(2)}$$

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

$$x+7=\log_{2}\left(21\right)$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x=\log_{2}\left(21\right)-7$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(2)}+\log_{2}\left(21\right)-7$$

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