3(2^x)-2=19 eching

$$3 ( 2 ^ { x } ) - 2 = 19$$

x uchun yechish

$$x=\log_{2}\left(7\right)\approx 2,807354922$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3\times 2^{x}-2=19$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$3\times 2^{x}=21$$

Ikki tarafini 3 ga bo‘ling.

$$2^{x}=7$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x})=\log(7)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(2)=\log(7)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x=\frac{\log(7)}{\log(2)}$$

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

$$x=\log_{2}\left(7\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(7\right)$$

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