14400=4000(1025)^x eching

$$14400 = 4000 ( 1025 ) ^ { x }$$

x uchun yechish

$$x=\log_{1025}\left(\frac{18}{5}\right)\approx 0,184773671$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 4000 ga bo‘ling.

$$\frac{14400}{4000}=1025^{x}$$

\frac{14400}{4000} ulushini 800 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{18}{5}=1025^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1025^{x}=\frac{18}{5}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(1025^{x})=\log(\frac{18}{5})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(1025)=\log(\frac{18}{5})$$

Ikki tarafini \log(1025) ga bo‘ling.

$$x=\frac{\log(\frac{18}{5})}{\log(1025)}$$

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

$$x=\log_{1025}\left(\frac{18}{5}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1025)}+\log_{1025}\left(\frac{18}{5}\right)$$

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