6^3r=36 eching

$$6 ^ { 3 r } = 36$$

r uchun yechish

$$r=\frac{2}{3}\approx 0,666666667$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$6^{3r}=36$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(6^{3r})=\log(36)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$3r\log(6)=\log(36)$$

Ikki tarafini \log(6) ga bo‘ling.

$$3r=\frac{\log(36)}{\log(6)}$$

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

$$3r=\log_{6}\left(36\right)$$

Ikki tarafini 3 ga bo‘ling.

$$r=\frac{2}{3}$$

r uchun yechish (complex solution)

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

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