Whakaoti i te 9000=3200(1.0775^x

$$9000=3200( { 1.0775 }^{ x }$$

Whakaoti mō x

$$x=\log_{1.0775}\left(2.8125\right)\approx 13.85349256$$

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

Whakawehea ngā taha e rua ki te 3200.

$$\frac{9000}{3200}=1.0775^{x}$$

Whakahekea te hautanga \frac{9000}{3200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 200.

$$\frac{45}{16}=1.0775^{x}$$

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

$$1.0775^{x}=\frac{45}{16}$$

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

$$\log(1.0775^{x})=\log(\frac{45}{16})$$

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

$$x\log(1.0775)=\log(\frac{45}{16})$$

Whakawehea ngā taha e rua ki te \log(1.0775).

$$x=\frac{\log(\frac{45}{16})}{\log(1.0775)}$$

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

$$x=\log_{1.0775}\left(\frac{45}{16}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.0775)}+\log_{1.0775}\left(2.8125\right)$$

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