3^x=5 eching

$$3 ^ { x } = 5$$

x uchun yechish

$$x=\log_{3}\left(5\right)\approx 1,464973521$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{x}=5$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(3) ga bo‘ling.

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

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

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

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(5\right)$$

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