2^2x+3=8 eching

$$2 ^ { 2 x + 3 } = 8$$

x uchun yechish

$$x=0$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{2x+3}=8$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x+3\right)\log(2)=\log(8)$$

Ikki tarafini \log(2) ga bo‘ling.

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

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

$$2x+3=\log_{2}\left(8\right)$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$2x=3-3$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{0}{2}$$

x uchun yechish (complex solution)

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

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