4^-x=37 eching

$$4 ^ { - x } = 37$$

x uchun yechish

$$x = -\frac{\log_{2} {(37)}}{2} \approx -2,604726683$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{-x}=37$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{-x})=\log(37)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-x\log(4)=\log(37)$$

Ikki tarafini \log(4) ga bo‘ling.

$$-x=\frac{\log(37)}{\log(4)}$$

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

$$-x=\log_{4}\left(37\right)$$

Ikki tarafini -1 ga bo‘ling.

$$x=\frac{\log_{2}\left(37\right)}{-2}$$

x uchun yechish (complex solution)

$$x=-\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(37\right)}{2}$$

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