Whakaoti i te 293=336e^r(39)

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

Whakaoti mō r

$$r=\frac{\ln(\frac{293}{336})}{39}\approx -0.003511245$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakawehea ngā taha e rua ki te 336.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

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

Tuhia te tau taupū kōaro o ngā taha e rua o te whārite.

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

Ko te taupū kōaro o tētahi tau ka hīkina ki tētahi pū ko te pū whakarea ki te taupū kōaro o taua tau.

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

Whakawehea ngā taha e rua ki te \log(e).

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

Mā te tikanga tātai huri pūtake \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

Whakawehea ngā taha e rua ki te 39.

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

Whakaoti mō r (complex solution)

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

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