2^31*4^50div2=4^5x eching

$${ 2 }^{ 31 } \times { 4 }^{ 50 } \div 2= { 4 }^{ 5x }$$

x uchun yechish

$$x=13$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$2^{31}\times 4^{50}=2\times 4^{5x}$$

31 daraja ko‘rsatkichini 2 ga hisoblang va 2147483648 ni qiymatni oling.

$$2147483648\times 4^{50}=2\times 4^{5x}$$

50 daraja ko‘rsatkichini 4 ga hisoblang va 1267650600228229401496703205376 ni qiymatni oling.

$$2147483648\times 1267650600228229401496703205376=2\times 4^{5x}$$

2722258935367507707706996859454145691648 hosil qilish uchun 2147483648 va 1267650600228229401496703205376 ni ko'paytirish.

$$2722258935367507707706996859454145691648=2\times 4^{5x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2\times 4^{5x}=2722258935367507707706996859454145691648$$

Ikki tarafini 2 ga bo‘ling.

$$4^{5x}=\frac{2722258935367507707706996859454145691648}{2}$$

1361129467683753853853498429727072845824 ni olish uchun 2722258935367507707706996859454145691648 ni 2 ga bo‘ling.

$$4^{5x}=1361129467683753853853498429727072845824$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{5x})=\log(1361129467683753853853498429727072845824)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$5x\log(4)=\log(1361129467683753853853498429727072845824)$$

Ikki tarafini \log(4) ga bo‘ling.

$$5x=\frac{\log(1361129467683753853853498429727072845824)}{\log(4)}$$

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

$$5x=\log_{4}\left(1361129467683753853853498429727072845824\right)$$

Ikki tarafini 5 ga bo‘ling.

$$x=\frac{65}{5}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{5\ln(2)}+13$$

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