e^frac{x{4}}=205 eching

$$e ^ { \frac { x } { 4 } } = 205$$

x uchun yechish

$$x=4\ln(205)\approx 21,292039917$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{\frac{1}{4}x}=205$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{\frac{1}{4}x})=\log(205)$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\frac{1}{4}x\log(e)=\log(205)$$

Ikki tarafini \log(e) ga bo‘ling.

$$\frac{1}{4}x=\frac{\log(205)}{\log(e)}$$

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

$$\frac{1}{4}x=\log_{e}\left(205\right)$$

Ikkala tarafini 4 ga ko‘paytiring.

$$x=\frac{\ln(205)}{\frac{1}{4}}$$

x uchun yechish (complex solution)

$$x=4\ln(205)+i\times 8\pi n_{1}$$

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