9^x=sqrt{9} eching

$$9 ^ { x } = \sqrt { 9 }$$

x uchun yechish

$$x=\frac{1}{2}=0,5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9^{x}=\sqrt{9}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{x})=\log(3)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(9)=\log(3)$$

Ikki tarafini \log(9) ga bo‘ling.

$$x=\frac{\log(3)}{\log(9)}$$

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

$$x=\log_{9}\left(3\right)$$

x uchun yechish (complex solution)

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

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