Whakaoti i te 5=(1+9.6%)^n

$$5 = ( 1 + 9.6 \% ) ^ { n }$$

Whakaoti mō n

$$n=\log_{1.096}\left(5\right)\approx 17.557404545$$

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

Whakarohaina te \frac{9.6}{100} mā te whakarea i te taurunga me te tauraro ki te 10.

$$5=\left(1+\frac{96}{1000}\right)^{n}$$

Whakahekea te hautanga \frac{96}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$5=\left(1+\frac{12}{125}\right)^{n}$$

Tāpirihia te 1 ki te \frac{12}{125}, ka \frac{137}{125}.

$$5=\left(\frac{137}{125}\right)^{n}$$

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

$$\left(\frac{137}{125}\right)^{n}=5$$

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

$$\log(\left(\frac{137}{125}\right)^{n})=\log(5)$$

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

$$n\log(\frac{137}{125})=\log(5)$$

Whakawehea ngā taha e rua ki te \log(\frac{137}{125}).

$$n=\frac{\log(5)}{\log(\frac{137}{125})}$$

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

$$n=\log_{\frac{137}{125}}\left(5\right)$$