Whakaoti i te 19000=9500e^0.01x

$$19000 = 9500 e ^ { 0.01 x }$$

Whakaoti mō x

$$x=100\ln(2)\approx 69.314718056$$

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

Whakawehea ngā taha e rua ki te 9500.

$$\frac{19000}{9500}=e^{0.01x}$$

Whakawehea te 19000 ki te 9500, kia riro ko 2.

$$2=e^{0.01x}$$

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

$$e^{0.01x}=2$$

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

$$\log(e^{0.01x})=\log(2)$$

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

$$0.01x\log(e)=\log(2)$$

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

$$0.01x=\frac{\log(2)}{\log(e)}$$

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

$$0.01x=\log_{e}\left(2\right)$$

Me whakarea ngā taha e rua ki te 100.

$$x=\frac{\ln(2)}{0.01}$$

Whakaoti mō x (complex solution)

$$x=100\ln(2)+i\times 200\pi n_{1}$$

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