4^x=32 eching

$$4 ^ { x } = 32$$

x uchun yechish

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

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{x}=32$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{x})=\log(32)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(4)=\log(32)$$

Ikki tarafini \log(4) ga bo‘ling.

$$x=\frac{\log(32)}{\log(4)}$$

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

$$x=\log_{4}\left(32\right)$$

x uchun yechish (complex solution)

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

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