100000000=67*1026^x eching

$$100000000 = 67 \times { 1026 }^{ x }$$

x uchun yechish

$$x=\log_{1026}\left(\frac{100000000}{67}\right)\approx 2,050356378$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 67 ga bo‘ling.

$$\frac{100000000}{67}=1026^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1026^{x}=\frac{100000000}{67}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(1026^{x})=\log(\frac{100000000}{67})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(1026)=\log(\frac{100000000}{67})$$

Ikki tarafini \log(1026) ga bo‘ling.

$$x=\frac{\log(\frac{100000000}{67})}{\log(1026)}$$

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

$$x=\log_{1026}\left(\frac{100000000}{67}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1026)}+\log_{1026}\left(\frac{100000000}{67}\right)$$

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