9^n+2=240+9 eching

$$9 ^ { n + 2 } = 240 + 9$$

n uchun yechish

$$n=\frac{\log_{3}\left(249\right)-4}{2}\approx 0,511101029$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$9^{n+2}=249$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(9^{n+2})=\log(249)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(n+2\right)\log(9)=\log(249)$$

Ikki tarafini \log(9) ga bo‘ling.

$$n+2=\frac{\log(249)}{\log(9)}$$

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

$$n+2=\log_{9}\left(249\right)$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$n=\frac{\log_{3}\left(249\right)}{2}-2$$