5*3^x=20 eching

$$5 \times { 3 }^{ x } =20$$

x uchun yechish

$$x=2\log_{3}\left(2\right)\approx 1,261859507$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5\times 3^{x}=20$$

Ikki tarafini 5 ga bo‘ling.

$$3^{x}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{x})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(3)=\log(4)$$

Ikki tarafini \log(3) ga bo‘ling.

$$x=\frac{\log(4)}{\log(3)}$$

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

$$x=\log_{3}\left(4\right)$$

x uchun yechish (complex solution)

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

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