5=1777^x eching

$$5= { 1777 }^{ x }$$

x uchun yechish

$$x=\log_{1777}\left(5\right)\approx 0,21508838$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1777^{x}=5$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(1777^{x})=\log(5)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(1777)=\log(5)$$

Ikki tarafini \log(1777) ga bo‘ling.

$$x=\frac{\log(5)}{\log(1777)}$$

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

$$x=\log_{1777}\left(5\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1777)}+\log_{1777}\left(5\right)$$

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