Whakaoti i te 20=50(.92)^x

$$20 = 50 ( .92 ) ^ { x }$$

Whakaoti mō x

$$x=\log_{0.92}\left(0.4\right)\approx 10.989122704$$

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

Whakawehea ngā taha e rua ki te 50.

$$\frac{20}{50}=0.92^{x}$$

Whakahekea te hautanga \frac{20}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$\frac{2}{5}=0.92^{x}$$

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

$$0.92^{x}=\frac{2}{5}$$

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

$$\log(0.92^{x})=\log(\frac{2}{5})$$

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

$$x\log(0.92)=\log(\frac{2}{5})$$

Whakawehea ngā taha e rua ki te \log(0.92).

$$x=\frac{\log(\frac{2}{5})}{\log(0.92)}$$

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

$$x=\log_{0.92}\left(\frac{2}{5}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.92)}+\log_{0.92}\left(0.4\right)$$

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