9^x=243 eching

$$9 ^ { x } = 243$$

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.

$$9^{x}=243$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{x})=\log(243)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(9)=\log(243)$$

Ikki tarafini \log(9) ga bo‘ling.

$$x=\frac{\log(243)}{\log(9)}$$

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

$$x=\log_{9}\left(243\right)$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(3)}+\frac{5}{2}$$

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