Whakaoti i te e^7x=21

$$e ^ { 7 x } = 21$$

Whakaoti mō x

$$x=\frac{\ln(21)}{7}\approx 0.434931777$$

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.

$$e^{7x}=21$$

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

$$\log(e^{7x})=\log(21)$$

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

$$7x\log(e)=\log(21)$$

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

$$7x=\frac{\log(21)}{\log(e)}$$

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

$$7x=\log_{e}\left(21\right)$$

Whakawehea ngā taha e rua ki te 7.

$$x=\frac{\ln(21)}{7}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{7}+\frac{\ln(21)}{7}$$

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