e^2x-9=0 eching

$${ e }^{ 2x } -9=0$$

x uchun yechish

$$x=\ln(3)\approx 1,098612289$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{2x}-9=0$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$e^{2x}=9$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{2x})=\log(9)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$2x\log(e)=\log(9)$$

Ikki tarafini \log(e) ga bo‘ling.

$$2x=\frac{\log(9)}{\log(e)}$$

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

$$2x=\log_{e}\left(9\right)$$

Ikki tarafini 2 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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