4^2x+3=1 eching

$$4 ^ { 2 x + 3 } = 1$$

x uchun yechish

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$4^{2x+3}=1$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(4^{2x+3})=\log(1)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x+3\right)\log(4)=\log(1)$$

Ikki tarafini \log(4) ga bo‘ling.

$$2x+3=\frac{\log(1)}{\log(4)}$$

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

$$2x+3=\log_{4}\left(1\right)$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$2x=-3$$

Ikki tarafini 2 ga bo‘ling.

$$x=-\frac{3}{2}$$

x uchun yechish (complex solution)

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

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