3^6x-3=81 eching

$$3 ^ { 6 x - 3 } = 81$$

x uchun yechish

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1,166666667$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{6x-3}=81$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{6x-3})=\log(81)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(6x-3\right)\log(3)=\log(81)$$

Ikki tarafini \log(3) ga bo‘ling.

$$6x-3=\frac{\log(81)}{\log(3)}$$

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

$$6x-3=\log_{3}\left(81\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$6x=4-\left(-3\right)$$

Ikki tarafini 6 ga bo‘ling.

$$x=\frac{7}{6}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{3\ln(3)}+\frac{7}{6}$$

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