5^x+3=25 eching

$$5 ^ { x + 3 } = 25$$

x uchun yechish

$$x=-1$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x+3}=25$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x+3})=\log(25)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+3\right)\log(5)=\log(25)$$

Ikki tarafini \log(5) ga bo‘ling.

$$x+3=\frac{\log(25)}{\log(5)}$$

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

$$x+3=\log_{5}\left(25\right)$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=2-3$$

x uchun yechish (complex solution)

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

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