Whakaoti i te e^3x=30

$$e ^ { 3 x } = 30$$

Whakaoti mō x

$$x=\frac{\ln(30)}{3}\approx 1.133732461$$

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.

$$e^{3x}=30$$

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

$$\log(e^{3x})=\log(30)$$

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

$$3x\log(e)=\log(30)$$

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

$$3x=\frac{\log(30)}{\log(e)}$$

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

$$3x=\log_{e}\left(30\right)$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{\ln(30)}{3}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3}+\frac{\ln(30)}{3}$$

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