Whakaoti i te 5469.78=4500*1.05^n

$$5469.78 = 4500 \times 1.05 ^ { n }$$

Whakaoti mō n

$$n=\log_{1.05}\left(\frac{91163}{75000}\right)\approx 4.000007026$$

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

Whakawehea ngā taha e rua ki te 4500.

$$\frac{5469.78}{4500}=1.05^{n}$$

Whakarohaina te \frac{5469.78}{4500} mā te whakarea i te taurunga me te tauraro ki te 100.

$$\frac{546978}{450000}=1.05^{n}$$

Whakahekea te hautanga \frac{546978}{450000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{91163}{75000}=1.05^{n}$$

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

$$1.05^{n}=\frac{91163}{75000}$$

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

$$\log(1.05^{n})=\log(\frac{91163}{75000})$$

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

$$n\log(1.05)=\log(\frac{91163}{75000})$$

Whakawehea ngā taha e rua ki te \log(1.05).

$$n=\frac{\log(\frac{91163}{75000})}{\log(1.05)}$$

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

$$n=\log_{1.05}\left(\frac{91163}{75000}\right)$$