3^n=4 eching

$$3 ^ { n } = 4$$

n uchun yechish

$$n=2\log_{3}\left(2\right)\approx 1,261859507$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{n}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{n})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(3)=\log(4)$$

Ikki tarafini \log(3) ga bo‘ling.

$$n=\frac{\log(4)}{\log(3)}$$

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

$$n=\log_{3}\left(4\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(3)}+2\log_{3}\left(2\right)$$

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