25^x=625 eching

$$25 ^ { x } = 625$$

x uchun yechish

$$x=2$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$25^{x}=625$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(25^{x})=\log(625)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(25)=\log(625)$$

Ikki tarafini \log(25) ga bo‘ling.

$$x=\frac{\log(625)}{\log(25)}$$

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

$$x=\log_{25}\left(625\right)$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(5)}+2$$

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