450=130{(e)^-71(x)} eching

$$450=130 {(e)^{ -71(x) }}$$

x uchun yechish

$$x=\frac{\ln(\frac{13}{45})}{71}\approx -0,017488917$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 130 ga bo‘ling.

$$\frac{450}{130}=e^{-71x}$$

\frac{450}{130} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{45}{13}=e^{-71x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$e^{-71x}=\frac{45}{13}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{-71x})=\log(\frac{45}{13})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-71x\log(e)=\log(\frac{45}{13})$$

Ikki tarafini \log(e) ga bo‘ling.

$$-71x=\frac{\log(\frac{45}{13})}{\log(e)}$$

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

$$-71x=\log_{e}\left(\frac{45}{13}\right)$$

Ikki tarafini -71 ga bo‘ling.

$$x=\frac{\ln(\frac{45}{13})}{-71}$$

x uchun yechish (complex solution)

$$x=-\frac{2\pi n_{1}i}{71}+\frac{\ln(\frac{13}{45})}{71}$$

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