Whakaoti i te 4=2*e^2x

$$4 = 2 \cdot e ^ { 2 x }$$

Whakaoti mō x

$$x=\frac{\ln(2)}{2}\approx 0.34657359$$

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

Whakawehea ngā taha e rua ki te 2.

$$\frac{4}{2}=e^{2x}$$

Whakawehea te 4 ki te 2, kia riro ko 2.

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

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

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

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

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

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

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

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

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

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

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

Whakawehea ngā taha e rua ki te 2.

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

Whakaoti mō x (complex solution)

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

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