Whakaoti i te e^-9x=7.2

$$e ^ { - 9 x } = 7.2$$

Whakaoti mō x

$$x=\frac{\ln(\frac{5}{36})}{9}\approx -0.219342336$$

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.

$$e^{-9x}=7.2$$

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

$$\log(e^{-9x})=\log(7.2)$$

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

$$-9x\log(e)=\log(7.2)$$

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

$$-9x=\frac{\log(7.2)}{\log(e)}$$

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

$$-9x=\log_{e}\left(7.2\right)$$

Whakawehea ngā taha e rua ki te -9.

$$x=\frac{\ln(\frac{36}{5})}{-9}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{9}+\frac{\ln(\frac{5}{36})}{9}$$

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