33^x=243 eching

$$33 ^ { x } = 243$$

x uchun yechish

$$x=5\log_{33}\left(3\right)\approx 1,571013746$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$33^{x}=243$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(33^{x})=\log(243)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(33)=\log(243)$$

Ikki tarafini \log(33) ga bo‘ling.

$$x=\frac{\log(243)}{\log(33)}$$

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

$$x=\log_{33}\left(243\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(33)}+5\log_{33}\left(3\right)$$

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