4096=2^N-1 eching

$$4096 = 2 ^ { N - 1 }$$

N uchun yechish

$$N=13$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2^{N-1}=4096$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{N-1})=\log(4096)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(N-1\right)\log(2)=\log(4096)$$

Ikki tarafini \log(2) ga bo‘ling.

$$N-1=\frac{\log(4096)}{\log(2)}$$

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

$$N-1=\log_{2}\left(4096\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$N=12-\left(-1\right)$$