5000=30000*2^t eching

$$5000 = 30000 \cdot 2 ^ { t }$$

t uchun yechish

$$t=-\log_{2}\left(6\right)\approx -2,584962501$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 30000 ga bo‘ling.

$$\frac{5000}{30000}=2^{t}$$

\frac{5000}{30000} ulushini 5000 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{6}=2^{t}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2^{t}=\frac{1}{6}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{t})=\log(\frac{1}{6})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$t\log(2)=\log(\frac{1}{6})$$

Ikki tarafini \log(2) ga bo‘ling.

$$t=\frac{\log(\frac{1}{6})}{\log(2)}$$

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

$$t=\log_{2}\left(\frac{1}{6}\right)$$