32^x+3=2 eching

$$32 ^ { x + 3 } = 2$$

x uchun yechish

$$x = -\frac{14}{5} = -2\frac{4}{5} = -2,8$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$32^{x+3}=2$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(32^{x+3})=\log(2)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+3\right)\log(32)=\log(2)$$

Ikki tarafini \log(32) ga bo‘ling.

$$x+3=\frac{\log(2)}{\log(32)}$$

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

$$x+3=\log_{32}\left(2\right)$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\frac{1}{5}-3$$

x uchun yechish (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{5\ln(2)}-\frac{14}{5}$$

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