3^x=8 eching

$$3 ^ { x } = 8$$

x uchun yechish

$$x=3\log_{3}\left(2\right)\approx 1,892789261$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{x}=8$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x})=\log(8)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(3)=\log(8)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x=\frac{\log(8)}{\log(3)}$$

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

$$x=\log_{3}\left(8\right)$$

x uchun yechish (complex solution)

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

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