12(2^x-5)=500 eching

$$12 ( 2 ^ { x - 5 } ) = 500$$

x uchun yechish

$$x=\log_{2}\left(\frac{125}{3}\right)+5\approx 10,380821784$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$12\times 2^{x-5}=500$$

Ikki tarafini 12 ga bo‘ling.

$$2^{x-5}=\frac{125}{3}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x-5})=\log(\frac{125}{3})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x-5\right)\log(2)=\log(\frac{125}{3})$$

Ikki tarafini \log(2) ga bo‘ling.

$$x-5=\frac{\log(\frac{125}{3})}{\log(2)}$$

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

$$x-5=\log_{2}\left(\frac{125}{3}\right)$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\ln(\frac{125}{3})}{\ln(2)}-\left(-5\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(\frac{125}{3}\right)+5$$

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