e^x+3=12 eching

$$e ^ { x + 3 } = 12$$

x uchun yechish

$$x=\ln(12)-3\approx -0,51509335$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{x+3}=12$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{x+3})=\log(12)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(x+3\right)\log(e)=\log(12)$$

Ikki tarafini \log(e) ga bo‘ling.

$$x+3=\frac{\log(12)}{\log(e)}$$

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

$$x+3=\log_{e}\left(12\right)$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\ln(12)-3$$

x uchun yechish (complex solution)

$$x=\ln(12)-3+2\pi n_{1}i$$

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