5^x-7=1/125 eching

$$5 ^ { x - 7 } = \frac { 1 } { 125 }$$

x uchun yechish

$$x=4$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x-7}=\frac{1}{125}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x-7})=\log(\frac{1}{125})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-7\right)\log(5)=\log(\frac{1}{125})$$

Ikki tarafini \log(5) ga bo‘ling.

$$x-7=\frac{\log(\frac{1}{125})}{\log(5)}$$

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

$$x-7=\log_{5}\left(\frac{1}{125}\right)$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$x=-3-\left(-7\right)$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(5)}+4$$

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