50.000=77e^14x eching

$$50.000 = 77 e ^ { 14 x }$$

x uchun yechish

$$x=\frac{\ln(\frac{50}{77})}{14}\approx -0,030841601$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 77 ga bo‘ling.

$$\frac{50}{77}=e^{14x}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$e^{14x}=\frac{50}{77}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{14x})=\log(\frac{50}{77})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$14x\log(e)=\log(\frac{50}{77})$$

Ikki tarafini \log(e) ga bo‘ling.

$$14x=\frac{\log(\frac{50}{77})}{\log(e)}$$

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

$$14x=\log_{e}\left(\frac{50}{77}\right)$$

Ikki tarafini 14 ga bo‘ling.

$$x=\frac{\ln(\frac{50}{77})}{14}$$

x uchun yechish (complex solution)

$$x=\frac{\pi n_{1}i}{7}+\frac{\ln(\frac{50}{77})}{14}$$

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