2e^x-1=11 eching

$$2 e ^ { x } - 1 = 11$$

x uchun yechish

$$x=\ln(6)\approx 1,791759469$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$2e^{x}-1=11$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$2e^{x}=12$$

Ikki tarafini 2 ga bo‘ling.

$$e^{x}=6$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{x})=\log(6)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$x\log(e)=\log(6)$$

Ikki tarafini \log(e) ga bo‘ling.

$$x=\frac{\log(6)}{\log(e)}$$

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

$$x=\log_{e}\left(6\right)$$

x uchun yechish (complex solution)

$$x=\ln(6)+2\pi n_{1}i$$

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