Whakaoti i te 8000=5000(1005){(e)^12x}

$$8000=5000(1005) {(e)^{ 12x }}$$

Whakaoti mō x

$$x=\frac{\ln(2)}{4}-\frac{\ln(5025)}{12}\approx -0.536894933$$

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

Whakareatia te 5000 ki te 1005, ka 5025000.

$$8000=5025000e^{12x}$$

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

$$5025000e^{12x}=8000$$

Whakawehea ngā taha e rua ki te 5025000.

$$e^{12x}=\frac{8000}{5025000}$$

Whakahekea te hautanga \frac{8000}{5025000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 1000.

$$e^{12x}=\frac{8}{5025}$$

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

$$\log(e^{12x})=\log(\frac{8}{5025})$$

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

$$12x\log(e)=\log(\frac{8}{5025})$$

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

$$12x=\frac{\log(\frac{8}{5025})}{\log(e)}$$

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

$$12x=\log_{e}\left(\frac{8}{5025}\right)$$

Whakawehea ngā taha e rua ki te 12.

$$x=\frac{\ln(\frac{8}{5025})}{12}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{6}+\frac{\ln(2)}{4}-\frac{\ln(5025)}{12}$$

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