5e^3x=15 eching

$$5 e ^ { 3 x } = 15$$

x uchun yechish

$$x=\frac{\ln(3)}{3}\approx 0,366204096$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$5e^{3x}=15$$

Ikki tarafini 5 ga bo‘ling.

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

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

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

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$3x\log(e)=\log(3)$$

Ikki tarafini \log(e) ga bo‘ling.

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

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

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

Ikki tarafini 3 ga bo‘ling.

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

x uchun yechish (complex solution)

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

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