2^x+2^x=2^18 eching

$${ 2 }^{ x } + { 2 }^{ x } = { 2 }^{ 18 }$$

x uchun yechish

$$x=17$$

Logaritm ifodasidan foydalanish qadamlari

2\times 2^{x} ni olish uchun 2^{x} va 2^{x} ni birlashtirish.

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

18 daraja ko‘rsatkichini 2 ga hisoblang va 262144 ni qiymatni oling.

$$2\times 2^{x}=262144$$

Ikki tarafini 2 ga bo‘ling.

$$2^{x}=\frac{262144}{2}$$

131072 ni olish uchun 262144 ni 2 ga bo‘ling.

$$2^{x}=131072$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x})=\log(131072)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(2)=\log(131072)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x=\frac{\log(131072)}{\log(2)}$$

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

$$x=\log_{2}\left(131072\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+17$$

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