5^n-1=25 eching

$$5 ^ { n - 1 } = 25$$

n uchun yechish

$$n=3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{n-1}=25$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{n-1})=\log(25)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(n-1\right)\log(5)=\log(25)$$

Ikki tarafini \log(5) ga bo‘ling.

$$n-1=\frac{\log(25)}{\log(5)}$$

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

$$n-1=\log_{5}\left(25\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$n=2-\left(-1\right)$$