Whakaoti i te e^4x=120

$$e ^ { 4 x } = 120$$

Whakaoti mō x

$$x=\frac{\ln(120)}{4}\approx 1.196872936$$

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.

$$e^{4x}=120$$

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

$$\log(e^{4x})=\log(120)$$

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

$$4x\log(e)=\log(120)$$

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

$$4x=\frac{\log(120)}{\log(e)}$$

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

$$4x=\log_{e}\left(120\right)$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{\ln(120)}{4}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\pi n_{1}}{2}+\frac{\ln(120)}{4}$$

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