2^x+1+1={100001}_{2} eching

$${ 2 }^{ x+1 } +1 = { 100001 }_{ 2 }$$

x uchun yechish

$$x=5\log_{2}\left(5\right)+4\approx 15,609640474$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{x+1}+1=100001$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$2^{x+1}=100000$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x+1})=\log(100000)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+1\right)\log(2)=\log(100000)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x+1=\frac{\log(100000)}{\log(2)}$$

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

$$x+1=\log_{2}\left(100000\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=5\log_{2}\left(10\right)-1$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+5\log_{2}\left(5\right)+4$$

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