(110)^n=1/3855 eching

$$( 110 ) ^ { n } = \frac { 1 } { 3855 }$$

n uchun yechish

$$n=-\log_{110}\left(3855\right)\approx -1,75665584$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$110^{n}=\frac{1}{3855}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(110^{n})=\log(\frac{1}{3855})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(110)=\log(\frac{1}{3855})$$

Ikki tarafini \log(110) ga bo‘ling.

$$n=\frac{\log(\frac{1}{3855})}{\log(110)}$$

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

$$n=\log_{110}\left(\frac{1}{3855}\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(110)}-\log_{110}\left(3855\right)$$

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