5^x=1/125 eching

$$5 ^ { x } = \frac { 1 } { 125 }$$

x uchun yechish

$$x=-3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x}=\frac{1}{125}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x})=\log(\frac{1}{125})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(5)=\log(\frac{1}{125})$$

Ikki tarafini \log(5) ga bo‘ling.

$$x=\frac{\log(\frac{1}{125})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{1}{125}\right)$$

x uchun yechish (complex solution)

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

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