e^-3x+1=4 eching

$${ e }^{ -3x+1 } =4$$

x uchun yechish

$$x=\frac{1-2\ln(2)}{3}\approx -0,128764787$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{-3x+1}=4$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{-3x+1})=\log(4)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\left(-3x+1\right)\log(e)=\log(4)$$

Ikki tarafini \log(e) ga bo‘ling.

$$-3x+1=\frac{\log(4)}{\log(e)}$$

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

$$-3x+1=\log_{e}\left(4\right)$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

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

Ikki tarafini -3 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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