4590=18*(2^k-1) eching

$$4590 = 18 * ( 2 ^ { k } - 1 )$$

k uchun yechish

$$k=8$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 18 ga bo‘ling.

$$\frac{4590}{18}=2^{k}-1$$

255 ni olish uchun 4590 ni 18 ga bo‘ling.

$$255=2^{k}-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2^{k}-1=255$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$2^{k}=256$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{k})=\log(256)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$k\log(2)=\log(256)$$

Ikki tarafini \log(2) ga bo‘ling.

$$k=\frac{\log(256)}{\log(2)}$$

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

$$k=\log_{2}\left(256\right)$$