Whakaoti i te 47000000div9428=1.23^x

$$47000000 \div 9428 = { 1.23 }^{ x }$$

Whakaoti mō x

$$x=\log_{1.23}\left(\frac{11750000}{2357}\right)\approx 41.128676945$$

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

Whakahekea te hautanga \frac{47000000}{9428} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{11750000}{2357}=1.23^{x}$$

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

$$1.23^{x}=\frac{11750000}{2357}$$

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

$$\log(1.23^{x})=\log(\frac{11750000}{2357})$$

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

$$x\log(1.23)=\log(\frac{11750000}{2357})$$

Whakawehea ngā taha e rua ki te \log(1.23).

$$x=\frac{\log(\frac{11750000}{2357})}{\log(1.23)}$$

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

$$x=\log_{1.23}\left(\frac{11750000}{2357}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.23)}+\log_{1.23}\left(\frac{11750000}{2357}\right)$$

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