2^-3x=64 eching

$$2 ^ { - 3 x } = 64$$

x uchun yechish

$$x=-2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{-3x}=64$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{-3x})=\log(64)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-3x\log(2)=\log(64)$$

Ikki tarafini \log(2) ga bo‘ling.

$$-3x=\frac{\log(64)}{\log(2)}$$

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

$$-3x=\log_{2}\left(64\right)$$

Ikki tarafini -3 ga bo‘ling.

$$x=\frac{6}{-3}$$

x uchun yechish (complex solution)

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

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