(11/10)^n=(11/10)^3 eching

$$( \frac { 11 } { 10 } ) ^ { n } = ( \frac { 11 } { 10 } ) ^ { 3 }$$

n uchun yechish

$$n=3$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$\left(\frac{11}{10}\right)^{n}=\frac{1331}{1000}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(\left(\frac{11}{10}\right)^{n})=\log(\frac{1331}{1000})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$n\log(\frac{11}{10})=\log(\frac{1331}{1000})$$

Ikki tarafini \log(\frac{11}{10}) ga bo‘ling.

$$n=\frac{\log(\frac{1331}{1000})}{\log(\frac{11}{10})}$$

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

$$n=\log_{\frac{11}{10}}\left(\frac{1331}{1000}\right)$$