3^n-1=131/8 eching

$${ 3 }^{ n-1 } = 13 \frac{ 1 }{ 8 }$$

n uchun yechish

$$n=\log_{3}\left(\frac{35}{8}\right)+2\approx 3,343428009$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$3^{n-1}=\frac{105}{8}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(3^{n-1})=\log(\frac{105}{8})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(n-1\right)\log(3)=\log(\frac{105}{8})$$

Ikki tarafini \log(3) ga bo‘ling.

$$n-1=\frac{\log(\frac{105}{8})}{\log(3)}$$

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

$$n-1=\log_{3}\left(\frac{105}{8}\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{\ln(\frac{105}{8})}{\ln(3)}-\left(-1\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(\frac{35}{8}\right)+2$$

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