Whakaoti i te e^x=9

$$e ^ { x } = 9$$

Whakaoti mō x

$$x=2\ln(3)\approx 2.197224577$$

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.

$$e^{x}=9$$

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

$$\log(e^{x})=\log(9)$$

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

$$x\log(e)=\log(9)$$

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

$$x=\frac{\log(9)}{\log(e)}$$

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

$$x=\log_{e}\left(9\right)$$

Whakaoti mō x (complex solution)

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

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