293=336e^r(39) eching

$$293 = 336 e ^ { r ( 39 ) }$$

r uchun yechish

$$r=\frac{\ln(\frac{293}{336})}{39}\approx -0,003511245$$

Logaritm ifodasidan foydalanish qadamlari

Ikki tarafini 336 ga bo‘ling.

$$\frac{293}{336}=e^{r\times 39}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$e^{r\times 39}=\frac{293}{336}$$

Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.

$$e^{39r}=\frac{293}{336}$$

Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.

$$\log(e^{39r})=\log(\frac{293}{336})$$

Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.

$$39r\log(e)=\log(\frac{293}{336})$$

Ikki tarafini \log(e) ga bo‘ling.

$$39r=\frac{\log(\frac{293}{336})}{\log(e)}$$

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

$$39r=\log_{e}\left(\frac{293}{336}\right)$$

Ikki tarafini 39 ga bo‘ling.

$$r=\frac{\ln(\frac{293}{336})}{39}$$

r uchun yechish (complex solution)

$$r=\frac{2\pi n_{1}i}{39}+\frac{\ln(\frac{293}{336})}{39}$$

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