e^2x=3 eching

$$e ^ { 2 x } = 3$$

x uchun yechish

$$x=\frac{\ln(3)}{2}\approx 0,549306144$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{2x}=3$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(e)=\log(3)$$

Ikki tarafini \log(e) ga bo‘ling.

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

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

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

Ikki tarafini 2 ga bo‘ling.

$$x=\frac{\ln(3)}{2}$$

x uchun yechish (complex solution)

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

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