e^5n=1/2 eching

$$e ^ { 5 n } = \frac { 1 } { 2 }$$

n uchun yechish

$$n=-\frac{\ln(2)}{5}\approx -0,138629436$$

Logaritm ifodasidan foydalanish qadamlari

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{5n}=\frac{1}{2}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{5n})=\log(\frac{1}{2})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$5n\log(e)=\log(\frac{1}{2})$$

Ikki tarafini \log(e) ga bo‘ling.

$$5n=\frac{\log(\frac{1}{2})}{\log(e)}$$

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

$$5n=\log_{e}\left(\frac{1}{2}\right)$$

Ikki tarafini 5 ga bo‘ling.

$$n=-\frac{\ln(2)}{5}$$

n uchun yechish (complex solution)

$$n=\frac{i\times 2\pi n_{1}}{5}-\frac{\ln(2)}{5}$$

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