e^2x-1=3 eching

$$e ^ { 2 x - 1 } = 3$$

x uchun yechish

$$x = \frac{\log_{e} {(3)} + 1}{2} \approx 1,049306144$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{2x-1}=3$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{2x-1})=\log(3)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(2x-1\right)\log(e)=\log(3)$$

Ikki tarafini \log(e) ga bo‘ling.

$$2x-1=\frac{\log(3)}{\log(e)}$$

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

$$2x-1=\log_{e}\left(3\right)$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$2x=\ln(3)-\left(-1\right)$$

Ikki tarafini 2 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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