2=1065^n eching

$$2 = 1065 ^ { n }$$

n uchun yechish

$$n=\log_{1065}\left(2\right)\approx 0,099436813$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1065^{n}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(1065^{n})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(1065)=\log(2)$$

Ikki tarafini \log(1065) ga bo‘ling.

$$n=\frac{\log(2)}{\log(1065)}$$

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

$$n=\log_{1065}\left(2\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(1065)}+\log_{1065}\left(2\right)$$

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