18*2^x=2 eching

$$18 \cdot 2 ^ { x } = 2$$

x uchun yechish

$$x=-2\log_{2}\left(3\right)\approx -3,169925001$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$18\times 2^{x}=2$$

Ikki tarafini 18 ga bo‘ling.

$$2^{x}=\frac{1}{9}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x})=\log(\frac{1}{9})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(2)=\log(\frac{1}{9})$$

Ikki tarafini \log(2) ga bo‘ling.

$$x=\frac{\log(\frac{1}{9})}{\log(2)}$$

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

$$x=\log_{2}\left(\frac{1}{9}\right)$$

x uchun yechish (complex solution)

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

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