391^12=2^x eching

$${ 391 }^{ 12 } = { 2 }^{ x }$$

x uchun yechish

$$x=12\log_{2}\left(391\right)\approx 103,332297568$$

Logaritm ifodasidan foydalanish qadamlari

12 daraja ko‘rsatkichini 391 ga hisoblang va 12767947514633659874603497973281 ni qiymatni oling.

$$12767947514633659874603497973281=2^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2^{x}=12767947514633659874603497973281$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x})=\log(12767947514633659874603497973281)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(2)=\log(12767947514633659874603497973281)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x=\frac{\log(12767947514633659874603497973281)}{\log(2)}$$

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

$$x=\log_{2}\left(12767947514633659874603497973281\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+12\log_{2}\left(391\right)$$

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