6^x=1/216 eching

$$6 ^ { x } = \frac { 1 } { 216 }$$

x uchun yechish

$$x=-3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6^{x}=\frac{1}{216}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(6^{x})=\log(\frac{1}{216})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(6)=\log(\frac{1}{216})$$

Ikki tarafini \log(6) ga bo‘ling.

$$x=\frac{\log(\frac{1}{216})}{\log(6)}$$

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

$$x=\log_{6}\left(\frac{1}{216}\right)$$

x uchun yechish (complex solution)

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

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