9(16)^2x=589824 eching

$$9 ( 16 ) ^ { 2 x } = 589824$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9\times 16^{2x}=589824$$

Ikki tarafini 9 ga bo‘ling.

$$16^{2x}=65536$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(16^{2x})=\log(65536)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(16)=\log(65536)$$

Ikki tarafini \log(16) ga bo‘ling.

$$2x=\frac{\log(65536)}{\log(16)}$$

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

$$2x=\log_{16}\left(65536\right)$$

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{4}{2}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(2)}+2$$

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