6^x=3 eching

$$6 ^ { x } = 3$$

x uchun yechish

$$x=\log_{6}\left(3\right)\approx 0,613147193$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6^{x}=3$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(6^{x})=\log(3)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(6)=\log(3)$$

Ikki tarafini \log(6) ga bo‘ling.

$$x=\frac{\log(3)}{\log(6)}$$

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

$$x=\log_{6}\left(3\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(6)}+\log_{6}\left(3\right)$$

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