25^n=100 eching

$$25 ^ { n } = 100$$

n uchun yechish

$$n=\log_{5}\left(10\right)\approx 1,430676558$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$25^{n}=100$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(25^{n})=\log(100)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(25)=\log(100)$$

Ikki tarafini \log(25) ga bo‘ling.

$$n=\frac{\log(100)}{\log(25)}$$

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

$$n=\log_{25}\left(100\right)$$

n uchun yechish (complex solution)

$$n=\frac{\pi n_{1}i}{\ln(5)}+\log_{5}\left(10\right)$$

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