20=50e^frac{10{3}x} eching

$$20 = 50 e ^ { \frac { 10 } { 3 } x }$$

x uchun yechish

$$x=\frac{3\ln(\frac{2}{5})}{10}\approx -0,27488722$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 50 ga bo‘ling.

$$\frac{20}{50}=e^{\frac{10}{3}x}$$

\frac{20}{50} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{5}=e^{\frac{10}{3}x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$e^{\frac{10}{3}x}=\frac{2}{5}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{\frac{10}{3}x})=\log(\frac{2}{5})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$\frac{10}{3}x\log(e)=\log(\frac{2}{5})$$

Ikki tarafini \log(e) ga bo‘ling.

$$\frac{10}{3}x=\frac{\log(\frac{2}{5})}{\log(e)}$$

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

$$\frac{10}{3}x=\log_{e}\left(\frac{2}{5}\right)$$

Tenglamaning ikki tarafini \frac{10}{3} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$x=\frac{\ln(\frac{2}{5})}{\frac{10}{3}}$$

x uchun yechish (complex solution)

$$x=\frac{3\pi n_{1}i}{5}+\frac{3\ln(\frac{2}{5})}{10}$$

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