Whakaoti i te e^-5x=7

$$e ^ { - 5 x } = 7$$

Whakaoti mō x

$$x=-\frac{\ln(7)}{5}\approx -0.38918203$$

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.

$$e^{-5x}=7$$

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

$$\log(e^{-5x})=\log(7)$$

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

$$-5x\log(e)=\log(7)$$

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

$$-5x=\frac{\log(7)}{\log(e)}$$

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

$$-5x=\log_{e}\left(7\right)$$

Whakawehea ngā taha e rua ki te -5.

$$x=\frac{\ln(7)}{-5}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{5}-\frac{\ln(7)}{5}$$

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