Whakaoti i te 14000=7000e^0.08x

$$14000 = 7000 e ^ { 0.08 x }$$

Whakaoti mō x

$$x=\frac{25\ln(2)}{2}\approx 8.664339757$$

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

Whakawehea ngā taha e rua ki te 7000.

$$\frac{14000}{7000}=e^{0.08x}$$

Whakawehea te 14000 ki te 7000, kia riro ko 2.

$$2=e^{0.08x}$$

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

$$e^{0.08x}=2$$

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

$$\log(e^{0.08x})=\log(2)$$

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

$$0.08x\log(e)=\log(2)$$

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

$$0.08x=\frac{\log(2)}{\log(e)}$$

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

$$0.08x=\log_{e}\left(2\right)$$

Whakawehea ngā taha e rua o te whārite ki te 0.08, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$x=\frac{\ln(2)}{0.08}$$

Whakaoti mō x (complex solution)

$$x=\frac{25\ln(2)}{2}+i\times 25\pi n_{1}$$

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