Whakaoti i te 2500=1500(1+.06)^x

$$2500 = 1500 ( 1 + .06 ) ^ { x }$$

Whakaoti mō x

$$x=\log_{1.06}\left(\frac{5}{3}\right)\approx 8.766692911$$

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

Whakawehea ngā taha e rua ki te 1500.

$$\frac{2500}{1500}=\left(1+0.06\right)^{x}$$

Whakahekea te hautanga \frac{2500}{1500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 500.

$$\frac{5}{3}=\left(1+0.06\right)^{x}$$

Tāpirihia te 1 ki te 0.06, ka 1.06.

$$\frac{5}{3}=1.06^{x}$$

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

$$1.06^{x}=\frac{5}{3}$$

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

$$\log(1.06^{x})=\log(\frac{5}{3})$$

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

$$x\log(1.06)=\log(\frac{5}{3})$$

Whakawehea ngā taha e rua ki te \log(1.06).

$$x=\frac{\log(\frac{5}{3})}{\log(1.06)}$$

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

$$x=\log_{1.06}\left(\frac{5}{3}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.06)}+\log_{1.06}\left(\frac{5}{3}\right)$$

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