(-3)(2)^n-1=-1536 eching

$$( - 3 ) ( 2 ) ^ { n - 1 } = - 1536$$

n uchun yechish

$$n=10$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini -3 ga bo‘ling.

$$2^{n-1}=\frac{-1536}{-3}$$

512 ni olish uchun -1536 ni -3 ga bo‘ling.

$$2^{n-1}=512$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{n-1})=\log(512)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(n-1\right)\log(2)=\log(512)$$

Ikki tarafini \log(2) ga bo‘ling.

$$n-1=\frac{\log(512)}{\log(2)}$$

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

$$n-1=\log_{2}\left(512\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$n=9-\left(-1\right)$$

n uchun yechish (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(2)}+10$$

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