47000000div9428=123^x eching

$$47000000 \div 9428 = { 123 }^{ x }$$

x uchun yechish

$$x=\log_{123}\left(\frac{11750000}{2357}\right)\approx 1,769304388$$

Logaritm ifodasidan foydalanish qadamlari

\frac{47000000}{9428} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{11750000}{2357}=123^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$123^{x}=\frac{11750000}{2357}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(123^{x})=\log(\frac{11750000}{2357})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(123)=\log(\frac{11750000}{2357})$$

Ikki tarafini \log(123) ga bo‘ling.

$$x=\frac{\log(\frac{11750000}{2357})}{\log(123)}$$

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

$$x=\log_{123}\left(\frac{11750000}{2357}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(\frac{11750000}{2357}\right)$$

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