20000=7000{(e)^20x} eching

$$20000=7000 {(e)^{ 20x }}$$

x uchun yechish

$$x=\frac{\ln(\frac{20}{7})}{20}\approx 0,052491106$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 7000 ga bo‘ling.

$$\frac{20000}{7000}=e^{20x}$$

\frac{20000}{7000} ulushini 1000 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{20}{7}=e^{20x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$e^{20x}=\frac{20}{7}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{20x})=\log(\frac{20}{7})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$20x\log(e)=\log(\frac{20}{7})$$

Ikki tarafini \log(e) ga bo‘ling.

$$20x=\frac{\log(\frac{20}{7})}{\log(e)}$$

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

$$20x=\log_{e}\left(\frac{20}{7}\right)$$

Ikki tarafini 20 ga bo‘ling.

$$x=\frac{\ln(\frac{20}{7})}{20}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{10}+\frac{\ln(\frac{20}{7})}{20}$$

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