2e^x=9 eching

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

x uchun yechish

$$x=-\ln(\frac{2}{9})\approx 1,504077397$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

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

Ikki tarafini 2 ga bo‘ling.

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

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

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

Ikki tarafini \log(e) ga bo‘ling.

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

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

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

x uchun yechish (complex solution)

$$x=-\ln(\frac{2}{9})+2\pi n_{1}i$$

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