25=510(5)^x eching

$$25 = 510 ( 5 ) ^ { x }$$

x uchun yechish

$$x=-\log_{5}\left(102\right)+1\approx -1,87365718$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 510 ga bo‘ling.

$$\frac{25}{510}=5^{x}$$

\frac{25}{510} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{102}=5^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$5^{x}=\frac{5}{102}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(5^{x})=\log(\frac{5}{102})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(5)=\log(\frac{5}{102})$$

Ikki tarafini \log(5) ga bo‘ling.

$$x=\frac{\log(\frac{5}{102})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{5}{102}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(\frac{5}{102}\right)$$

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