Whakaoti i te 500=200*1.03^2x

$$500 = 200 \times 1.03 ^ { 2 x }$$

Whakaoti mō x

$$x = \frac{\log_{1.03} {(2.5)}}{2} \approx 15.499456378$$

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

Whakawehea ngā taha e rua ki te 200.

$$\frac{500}{200}=1.03^{2x}$$

Whakahekea te hautanga \frac{500}{200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 100.

$$\frac{5}{2}=1.03^{2x}$$

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

$$1.03^{2x}=\frac{5}{2}$$

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

$$\log(1.03^{2x})=\log(\frac{5}{2})$$

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

$$2x\log(1.03)=\log(\frac{5}{2})$$

Whakawehea ngā taha e rua ki te \log(1.03).

$$2x=\frac{\log(\frac{5}{2})}{\log(1.03)}$$

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

$$2x=\log_{1.03}\left(\frac{5}{2}\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\ln(\frac{5}{2})}{2\ln(\frac{103}{100})}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(1.03)}+\frac{\log_{1.03}\left(2.5\right)}{2}$$

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