9600=1500*2^x eching

$$9600=1500 \times { 2 }^{ x }$$

x uchun yechish

$$x=-\log_{2}\left(5\right)+5\approx 2,678071905$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 1500 ga bo‘ling.

$$\frac{9600}{1500}=2^{x}$$

\frac{9600}{1500} ulushini 300 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{32}{5}=2^{x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2^{x}=\frac{32}{5}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x})=\log(\frac{32}{5})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(2)=\log(\frac{32}{5})$$

Ikki tarafini \log(2) ga bo‘ling.

$$x=\frac{\log(\frac{32}{5})}{\log(2)}$$

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

$$x=\log_{2}\left(\frac{32}{5}\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}-\log_{2}\left(5\right)+5$$

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