Whakaoti i te 20000=7000{(e)^20x}

$$20000=7000 {(e)^{ 20x }}$$

Whakaoti mō x

$$x=\frac{\ln(\frac{20}{7})}{20}\approx 0.052491106$$

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

Whakawehea ngā taha e rua ki te 7000.

$$\frac{20000}{7000}=e^{20x}$$

Whakahekea te hautanga \frac{20000}{7000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 1000.

$$\frac{20}{7}=e^{20x}$$

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

$$e^{20x}=\frac{20}{7}$$

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

$$\log(e^{20x})=\log(\frac{20}{7})$$

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

$$20x\log(e)=\log(\frac{20}{7})$$

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

$$20x=\frac{\log(\frac{20}{7})}{\log(e)}$$

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

$$20x=\log_{e}\left(\frac{20}{7}\right)$$

Whakawehea ngā taha e rua ki te 20.

$$x=\frac{\ln(\frac{20}{7})}{20}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{10}+\frac{\ln(\frac{20}{7})}{20}$$

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