2^-x=32 eching

$$2 ^ { - x } = 32$$

x uchun yechish

$$x=-5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{-x}=32$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{-x})=\log(32)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-x\log(2)=\log(32)$$

Ikki tarafini \log(2) ga bo‘ling.

$$-x=\frac{\log(32)}{\log(2)}$$

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

$$-x=\log_{2}\left(32\right)$$

Ikki tarafini -1 ga bo‘ling.

$$x=\frac{5}{-1}$$

x uchun yechish (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{\ln(2)}-5$$

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