8000=5000(1005){(e)^12x} eching

$$8000=5000(1005) {(e)^{ 12x }}$$

x uchun yechish

$$x=\frac{\ln(2)}{4}-\frac{\ln(5025)}{12}\approx -0,536894933$$

Logaritm ifodasidan foydalanish qadamlari

5025000 hosil qilish uchun 5000 va 1005 ni ko'paytirish.

$$8000=5025000e^{12x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$5025000e^{12x}=8000$$

Ikki tarafini 5025000 ga bo‘ling.

$$e^{12x}=\frac{8000}{5025000}$$

\frac{8000}{5025000} ulushini 1000 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$e^{12x}=\frac{8}{5025}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{12x})=\log(\frac{8}{5025})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$12x\log(e)=\log(\frac{8}{5025})$$

Ikki tarafini \log(e) ga bo‘ling.

$$12x=\frac{\log(\frac{8}{5025})}{\log(e)}$$

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

$$12x=\log_{e}\left(\frac{8}{5025}\right)$$

Ikki tarafini 12 ga bo‘ling.

$$x=\frac{\ln(\frac{8}{5025})}{12}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{6}+\frac{\ln(2)}{4}-\frac{\ln(5025)}{12}$$

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