25=17+2^x eching

$$25 = 17 + 2 ^ { x }$$

x uchun yechish

$$x=3$$

Logaritm ifodasidan foydalanish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$17+2^{x}=25$$

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2^{x}+17=25$$

Tenglamaning ikkala tarafidan 17 ni ayirish.

$$2^{x}=8$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(2^{x})=\log(8)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(2)=\log(8)$$

Ikki tarafini \log(2) ga bo‘ling.

$$x=\frac{\log(8)}{\log(2)}$$

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

$$x=\log_{2}\left(8\right)$$

x uchun yechish (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+3$$

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