5^x=256 eching

$$5 ^ { x } = 256$$

x uchun yechish

$$x=8\log_{5}\left(2\right)\approx 3,445412465$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5^{x}=256$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x})=\log(256)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(5)=\log(256)$$

Ikki tarafini \log(5) ga bo‘ling.

$$x=\frac{\log(256)}{\log(5)}$$

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

$$x=\log_{5}\left(256\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+8\log_{5}\left(2\right)$$

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