1/5e^6x=4 eching

$$\frac { 1 } { 5 } e ^ { 6 x } = 4$$

x uchun yechish

$$x=\frac{\ln(20)}{6}\approx 0,499288712$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$\frac{1}{5}e^{6x}=4$$

Ikkala tarafini 5 ga ko‘paytiring.

$$e^{6x}=20$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{6x})=\log(20)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$6x\log(e)=\log(20)$$

Ikki tarafini \log(e) ga bo‘ling.

$$6x=\frac{\log(20)}{\log(e)}$$

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

$$6x=\log_{e}\left(20\right)$$

Ikki tarafini 6 ga bo‘ling.

$$x=\frac{\ln(20)}{6}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{3}+\frac{\ln(20)}{6}$$

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