Whakaoti i te e^2x-1=3

$$e ^ { 2 x - 1 } = 3$$

Whakaoti mō x

$$x = \frac{\log_{e} {(3)} + 1}{2} \approx 1.049306144$$

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

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$e^{2x-1}=3$$

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

$$\log(e^{2x-1})=\log(3)$$

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

$$\left(2x-1\right)\log(e)=\log(3)$$

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

$$2x-1=\frac{\log(3)}{\log(e)}$$

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

$$2x-1=\log_{e}\left(3\right)$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$2x=\ln(3)-\left(-1\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\ln(3)+1}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\ln(3)+1}{2}+i\pi n_{1}$$

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