5^x+2=125 eching

$$5 ^ { x + 2 } = 125$$

x uchun yechish

$$x=1$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x+2}=125$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x+2})=\log(125)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+2\right)\log(5)=\log(125)$$

Ikki tarafini \log(5) ga bo‘ling.

$$x+2=\frac{\log(125)}{\log(5)}$$

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

$$x+2=\log_{5}\left(125\right)$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=3-2$$

x uchun yechish (complex solution)

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

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