3^x=1/6 eching

$$3 ^ { x } = \frac { 1 } { 6 }$$

x uchun yechish

$$x=-\log_{3}\left(6\right)\approx -1,630929754$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{x}=\frac{1}{6}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x})=\log(\frac{1}{6})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(3)=\log(\frac{1}{6})$$

Ikki tarafini \log(3) ga bo‘ling.

$$x=\frac{\log(\frac{1}{6})}{\log(3)}$$

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

$$x=\log_{3}\left(\frac{1}{6}\right)$$

x uchun yechish (complex solution)

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

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