16^x=64 eching

$$16 ^ { x } = 64$$

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.

$$16^{x}=64$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(16^{x})=\log(64)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(16)=\log(64)$$

Ikki tarafini \log(16) ga bo‘ling.

$$x=\frac{\log(64)}{\log(16)}$$

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

$$x=\log_{16}\left(64\right)$$

x uchun yechish (complex solution)

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

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