3=(106)^x eching

$$3 = ( 106 ) ^ { x }$$

x uchun yechish

$$x=\log_{106}\left(3\right)\approx 0,235579851$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$106^{x}=3$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(106^{x})=\log(3)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(106)=\log(3)$$

Ikki tarafini \log(106) ga bo‘ling.

$$x=\frac{\log(3)}{\log(106)}$$

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

$$x=\log_{106}\left(3\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(106)}+\log_{106}\left(3\right)$$

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