Whakaoti i te 71=910(0.895)^3x

$$71 = 910 ( 0.895 ) ^ { 3 x }$$

Whakaoti mō x

$$x = \frac{\log_{\frac{200}{179}} {(\frac{910}{71})}}{3} \approx 7.664679935$$

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

Whakawehea ngā taha e rua ki te 910.

$$\frac{71}{910}=0.895^{3x}$$

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

$$0.895^{3x}=\frac{71}{910}$$

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

$$\log(0.895^{3x})=\log(\frac{71}{910})$$

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

$$3x\log(0.895)=\log(\frac{71}{910})$$

Whakawehea ngā taha e rua ki te \log(0.895).

$$3x=\frac{\log(\frac{71}{910})}{\log(0.895)}$$

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

$$3x=\log_{0.895}\left(\frac{71}{910}\right)$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{\ln(\frac{71}{910})}{3\ln(\frac{179}{200})}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(0.895)}+\frac{\log_{0.895}\left(\frac{71}{910}\right)}{3}$$

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