Whakaoti i te 450=130{(e)^-71(x)}

$$450=130 {(e)^{ -71(x) }}$$

Whakaoti mō x

$$x=\frac{\ln(\frac{13}{45})}{71}\approx -0.017488917$$

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

Whakawehea ngā taha e rua ki te 130.

$$\frac{450}{130}=e^{-71x}$$

Whakahekea te hautanga \frac{450}{130} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$\frac{45}{13}=e^{-71x}$$

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

$$e^{-71x}=\frac{45}{13}$$

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

$$\log(e^{-71x})=\log(\frac{45}{13})$$

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

$$-71x\log(e)=\log(\frac{45}{13})$$

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

$$-71x=\frac{\log(\frac{45}{13})}{\log(e)}$$

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

$$-71x=\log_{e}\left(\frac{45}{13}\right)$$

Whakawehea ngā taha e rua ki te -71.

$$x=\frac{\ln(\frac{45}{13})}{-71}$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\pi n_{1}i}{71}+\frac{\ln(\frac{13}{45})}{71}$$

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