1000000=418658*left(10250right)^x eching

$$1000000=418658 \times { \left(10250 \right) }^{ x }$$

x uchun yechish

$$x=\log_{10250}\left(\frac{500000}{209329}\right)\approx 0,094282383$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 418658 ga bo‘ling.

$$\frac{1000000}{418658}=10250^{x}$$

\frac{1000000}{418658} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{500000}{209329}=10250^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$10250^{x}=\frac{500000}{209329}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(10250^{x})=\log(\frac{500000}{209329})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(10250)=\log(\frac{500000}{209329})$$

Ikki tarafini \log(10250) ga bo‘ling.

$$x=\frac{\log(\frac{500000}{209329})}{\log(10250)}$$

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

$$x=\log_{10250}\left(\frac{500000}{209329}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10250)}+\log_{10250}\left(\frac{500000}{209329}\right)$$

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