12^y-6=3 eching

$$12 ^ { y - 6 } = 3$$

y uchun yechish

$$y=\log_{12}\left(8957952\right)\approx 6,442114109$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$12^{y-6}=3$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(12^{y-6})=\log(3)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(y-6\right)\log(12)=\log(3)$$

Ikki tarafini \log(12) ga bo‘ling.

$$y-6=\frac{\log(3)}{\log(12)}$$

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

$$y-6=\log_{12}\left(3\right)$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$y=\log_{12}\left(3\right)-\left(-6\right)$$

y uchun yechish (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(12)}+\log_{12}\left(8957952\right)$$

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