3^x=2020 eching

$${ 3 }^{ x } =2020$$

x uchun yechish

$$x=\log_{3}\left(2020\right)\approx 6,927696758$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{x}=2020$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x})=\log(2020)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(3)=\log(2020)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x=\frac{\log(2020)}{\log(3)}$$

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

$$x=\log_{3}\left(2020\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(2020\right)$$

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