Whakaoti i te e^1x=7

$$e ^ { 1 x } = 7$$

Whakaoti mō x

$$x=\ln(7)\approx 1.945910149$$

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.

$$e^{x}=7$$

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

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

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

$$x\log(e)=\log(7)$$

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

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

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

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

Whakaoti mō x (complex solution)

$$x=\ln(7)+2\pi n_{1}i$$

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