8*31^x=80 eching

$$8 \times 31 ^ { x } = 80$$

x uchun yechish

$$x=\log_{31}\left(10\right)\approx 0,670528152$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$8\times 31^{x}=80$$

Ikki tarafini 8 ga bo‘ling.

$$31^{x}=10$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(31^{x})=\log(10)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(31)=\log(10)$$

Ikki tarafini \log(31) ga bo‘ling.

$$x=\frac{\log(10)}{\log(31)}$$

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

$$x=\log_{31}\left(10\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(31)}+\log_{31}\left(10\right)$$

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