112^n=2 eching

$$112 ^ { n } = 2$$

n uchun yechish

$$n=\log_{112}\left(2\right)\approx 0,146899936$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$112^{n}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(112^{n})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(112)=\log(2)$$

Ikki tarafini \log(112) ga bo‘ling.

$$n=\frac{\log(2)}{\log(112)}$$

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

$$n=\log_{112}\left(2\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(112)}+\log_{112}\left(2\right)$$

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