20=50(92)^x eching

$$20 = 50 ( 92 ) ^ { x }$$

x uchun yechish

$$x=\log_{92}\left(\frac{2}{5}\right)\approx -0,202639004$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 50 ga bo‘ling.

$$\frac{20}{50}=92^{x}$$

\frac{20}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{5}=92^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$92^{x}=\frac{2}{5}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(92^{x})=\log(\frac{2}{5})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(92)=\log(\frac{2}{5})$$

Ikki tarafini \log(92) ga bo‘ling.

$$x=\frac{\log(\frac{2}{5})}{\log(92)}$$

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

$$x=\log_{92}\left(\frac{2}{5}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(92)}+\log_{92}\left(\frac{2}{5}\right)$$

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