Whakaoti i te 0.25={(e)^-2x}

$$0.25= {(e)^{ -2x }}$$

Whakaoti mō x

$$x=\ln(2)\approx 0.693147181$$

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

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

$$e^{-2x}=0.25$$

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

$$\log(e^{-2x})=\log(0.25)$$

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

$$-2x\log(e)=\log(0.25)$$

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

$$-2x=\frac{\log(0.25)}{\log(e)}$$

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

$$-2x=\log_{e}\left(0.25\right)$$

Whakawehea ngā taha e rua ki te -2.

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

Whakaoti mō x (complex solution)

$$x=-i\pi n_{1}+\ln(2)$$

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