5^x-125=0 eching

$$5 ^ { x } - 125 = 0$$

x uchun yechish

$$x=3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x}-125=0$$

125 ni tenglamaning ikkala tarafiga qo'shish.

$$5^{x}=125$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x})=\log(125)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(5)=\log(125)$$

Ikki tarafini \log(5) ga bo‘ling.

$$x=\frac{\log(125)}{\log(5)}$$

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

$$x=\log_{5}\left(125\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+3$$

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