Whakaoti i te 2700=1800e^19h

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

Whakaoti mō h

$$h=\frac{\ln(\frac{3}{2})}{19}\approx 0.021340269$$

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

Whakawehea ngā taha e rua ki te 1800.

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

Whakahekea te hautanga \frac{2700}{1800} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 900.

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

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

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

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

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

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

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

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

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

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

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

Whakawehea ngā taha e rua ki te 19.

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

Whakaoti mō h (complex solution)

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

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