Whakaoti i te e^-x=5

$${ e }^{ -x } =5$$

Whakaoti mō x

$$x=-\ln(5)\approx -1.609437912$$

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.

$$e^{-x}=5$$

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

$$\log(e^{-x})=\log(5)$$

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

$$-x\log(e)=\log(5)$$

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

$$-x=\frac{\log(5)}{\log(e)}$$

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

$$-x=\log_{e}\left(5\right)$$

Whakawehea ngā taha e rua ki te -1.

$$x=\frac{\ln(5)}{-1}$$

Whakaoti mō x (complex solution)

$$x=-2\pi n_{1}i-\ln(5)$$

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