2700=1800e^19h eching

$$2700 = 1800 e ^ { 19 h }$$

h uchun yechish

$$h=\frac{\ln(\frac{3}{2})}{19}\approx 0,021340269$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 1800 ga bo‘ling.

$$\frac{2700}{1800}=e^{19h}$$

\frac{2700}{1800} ulushini 900 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3}{2}=e^{19h}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$e^{19h}=\frac{3}{2}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{19h})=\log(\frac{3}{2})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$19h\log(e)=\log(\frac{3}{2})$$

Ikki tarafini \log(e) ga bo‘ling.

$$19h=\frac{\log(\frac{3}{2})}{\log(e)}$$

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

$$19h=\log_{e}\left(\frac{3}{2}\right)$$

Ikki tarafini 19 ga bo‘ling.

$$h=\frac{\ln(\frac{3}{2})}{19}$$

h uchun yechish (complex solution)

$$h=\frac{2\pi n_{1}i}{19}+\frac{\ln(\frac{3}{2})}{19}$$

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