e^4x=120 eching

$$e ^ { 4 x } = 120$$

x uchun yechish

$$x=\frac{\ln(120)}{4}\approx 1,196872936$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{4x}=120$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{4x})=\log(120)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$4x\log(e)=\log(120)$$

Ikki tarafini \log(e) ga bo‘ling.

$$4x=\frac{\log(120)}{\log(e)}$$

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

$$4x=\log_{e}\left(120\right)$$

Ikki tarafini 4 ga bo‘ling.

$$x=\frac{\ln(120)}{4}$$

x uchun yechish (complex solution)

$$x=\frac{i\pi n_{1}}{2}+\frac{\ln(120)}{4}$$

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