28=36e^-k10 eching

$$28 = 36 e ^ { - k 10 }$$

k_10 uchun yechish

$$k_{10}=\ln(\frac{9}{7})\approx 0,251314428$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 36 ga bo‘ling.

$$\frac{28}{36}=e^{-k_{10}}$$

\frac{28}{36} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{7}{9}=e^{-k_{10}}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$e^{-k_{10}}=\frac{7}{9}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{-k_{10}})=\log(\frac{7}{9})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$-k_{10}\log(e)=\log(\frac{7}{9})$$

Ikki tarafini \log(e) ga bo‘ling.

$$-k_{10}=\frac{\log(\frac{7}{9})}{\log(e)}$$

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

$$-k_{10}=\log_{e}\left(\frac{7}{9}\right)$$

Ikki tarafini -1 ga bo‘ling.

$$k_{10}=\frac{\ln(\frac{7}{9})}{-1}$$

k_10 uchun yechish (complex solution)

$$k_{10}=-2\pi n_{1}i+\ln(\frac{9}{7})$$

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