(7^2)^n=497^8 eching

$$( 7 ^ { 2 } ) ^ { n } = 497 ^ { 8 }$$

n uchun yechish

$$n=4\log_{7}\left(497\right)\approx 12,762336491$$

Logaritm ifodasidan foydalanish qadamlari

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$49^{n}=497^{8}$$

8 daraja ko‘rsatkichini 497 ga hisoblang va 3722640602679094258561 ni qiymatni oling.

$$49^{n}=3722640602679094258561$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(49^{n})=\log(3722640602679094258561)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(49)=\log(3722640602679094258561)$$

Ikki tarafini \log(49) ga bo‘ling.

$$n=\frac{\log(3722640602679094258561)}{\log(49)}$$

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

$$n=\log_{49}\left(3722640602679094258561\right)$$