8^5x=3 eching

$$8 ^ { 5 x } = 3$$

x uchun yechish

$$x=\frac{\log_{2}\left(3\right)}{15}\approx 0,105664167$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$8^{5x}=3$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(8^{5x})=\log(3)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$5x\log(8)=\log(3)$$

Ikki tarafini \log(8) ga bo‘ling.

$$5x=\frac{\log(3)}{\log(8)}$$

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

$$5x=\log_{8}\left(3\right)$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{\log_{2}\left(3\right)}{3\times 5}$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{15\ln(2)}+\frac{\log_{2}\left(3\right)}{15}$$

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