(5825)^(x-3)=120 eching

$$( 5825 ) ^ { ( x - 3 ) } = 120$$

x uchun yechish

$$x=\log_{5825}\left(23717506875000\right)\approx 3,552195972$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5825^{x-3}=120$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5825^{x-3})=\log(120)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-3\right)\log(5825)=\log(120)$$

Ikki tarafini \log(5825) ga bo‘ling.

$$x-3=\frac{\log(120)}{\log(5825)}$$

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

$$x-3=\log_{5825}\left(120\right)$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\log_{5825}\left(120\right)-\left(-3\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5825)}+\log_{5825}\left(23717506875000\right)$$

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