2^-2x=8 eching

$$2 ^ { - 2 x } = 8$$

x uchun yechish

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{-2x}=8$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-2x\log(2)=\log(8)$$

Ikki tarafini \log(2) ga bo‘ling.

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

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

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

Ikki tarafini -2 ga bo‘ling.

$$x=\frac{3}{-2}$$

x uchun yechish (complex solution)

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

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