5^2x+2=1/625 eching

$$5 ^ { 2 x + 2 } = \frac { 1 } { 625 }$$

x uchun yechish

$$x=-3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{2x+2}=\frac{1}{625}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{2x+2})=\log(\frac{1}{625})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x+2\right)\log(5)=\log(\frac{1}{625})$$

Ikki tarafini \log(5) ga bo‘ling.

$$2x+2=\frac{\log(\frac{1}{625})}{\log(5)}$$

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

$$2x+2=\log_{5}\left(\frac{1}{625}\right)$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$2x=-4-2$$

Ikki tarafini 2 ga bo‘ling.

$$x=-\frac{6}{2}$$