4^y-9=15 eching

$$4 ^ { y - 9 } = 15$$

y uchun yechish

$$y = \frac{\log_{2} {(15)} + 18}{2} \approx 10,953445298$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{y-9}=15$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{y-9})=\log(15)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(y-9\right)\log(4)=\log(15)$$

Ikki tarafini \log(4) ga bo‘ling.

$$y-9=\frac{\log(15)}{\log(4)}$$

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

$$y-9=\log_{4}\left(15\right)$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$y=\frac{\log_{2}\left(15\right)}{2}-\left(-9\right)$$

y uchun yechish (complex solution)

$$y=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(15\right)}{2}+9$$

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