9000=3200(10775^x eching

$$9000=3200( { 10775 }^{ x }$$

x uchun yechish

$$x=\log_{10775}\left(\frac{45}{16}\right)\approx 0,11137055$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 3200 ga bo‘ling.

$$\frac{9000}{3200}=10775^{x}$$

\frac{9000}{3200} ulushini 200 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{45}{16}=10775^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$10775^{x}=\frac{45}{16}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(10775^{x})=\log(\frac{45}{16})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(10775)=\log(\frac{45}{16})$$

Ikki tarafini \log(10775) ga bo‘ling.

$$x=\frac{\log(\frac{45}{16})}{\log(10775)}$$

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

$$x=\log_{10775}\left(\frac{45}{16}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10775)}+\log_{10775}\left(\frac{45}{16}\right)$$

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