Whakaoti i te 23=40e^-0.2h

$$23 = 40 e ^ { - 0.2 h }$$

Whakaoti mō h

$$h=\ln(\frac{102400000}{6436343})\approx 2.766926191$$

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

Whakawehea ngā taha e rua ki te 40.

$$\frac{23}{40}=e^{-0.2h}$$

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

$$e^{-0.2h}=\frac{23}{40}$$

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

$$\log(e^{-0.2h})=\log(\frac{23}{40})$$

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

$$-0.2h\log(e)=\log(\frac{23}{40})$$

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

$$-0.2h=\frac{\log(\frac{23}{40})}{\log(e)}$$

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

$$-0.2h=\log_{e}\left(\frac{23}{40}\right)$$

Me whakarea ngā taha e rua ki te -5.

$$h=\frac{\ln(\frac{23}{40})}{-0.2}$$

Whakaoti mō h (complex solution)

$$h=-i\times 10\pi n_{1}+\ln(\frac{102400000}{6436343})$$

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