Whakaoti i te e^x-4=2

$$e ^ { x - 4 } = 2$$

Whakaoti mō x

$$x=\ln(2)+4\approx 4.693147181$$

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.

$$e^{x-4}=2$$

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

$$\log(e^{x-4})=\log(2)$$

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

$$\left(x-4\right)\log(e)=\log(2)$$

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

$$x-4=\frac{\log(2)}{\log(e)}$$

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

$$x-4=\log_{e}\left(2\right)$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=\ln(2)-\left(-4\right)$$

Whakaoti mō x (complex solution)

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

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