Whakaoti i te e^-9x=72

$$e ^ { - 9 x } = 72$$

Whakaoti mō x

$$x=-\frac{\ln(72)}{9}\approx -0.475185124$$

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.

$$e^{-9x}=72$$

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

$$\log(e^{-9x})=\log(72)$$

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

$$-9x\log(e)=\log(72)$$

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

$$-9x=\frac{\log(72)}{\log(e)}$$

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

$$-9x=\log_{e}\left(72\right)$$

Whakawehea ngā taha e rua ki te -9.

$$x=\frac{\ln(72)}{-9}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{9}-\frac{\ln(72)}{9}$$

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