105^n=700 eching

$$105 ^ { n } = 700$$

n uchun yechish

$$n=\log_{105}\left(700\right)\approx 1,407635614$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$105^{n}=700$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(105^{n})=\log(700)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(105)=\log(700)$$

Ikki tarafini \log(105) ga bo‘ling.

$$n=\frac{\log(700)}{\log(105)}$$

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

$$n=\log_{105}\left(700\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(105)}+\log_{105}\left(700\right)$$

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