6^3x=216 eching

$$6 ^ { 3 x } = 216$$

x uchun yechish

$$x=1$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6^{3x}=216$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(6^{3x})=\log(216)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$3x\log(6)=\log(216)$$

Ikki tarafini \log(6) ga bo‘ling.

$$3x=\frac{\log(216)}{\log(6)}$$

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

$$3x=\log_{6}\left(216\right)$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{3}{3}$$

x uchun yechish (complex solution)

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

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