Whakaoti i te e^y-6=8

$$e ^ { y - 6 } = 8$$

Whakaoti mō y

$$y=3\left(\ln(2)+2\right)\approx 8.079441542$$

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.

$$e^{y-6}=8$$

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

$$\log(e^{y-6})=\log(8)$$

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

$$\left(y-6\right)\log(e)=\log(8)$$

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

$$y-6=\frac{\log(8)}{\log(e)}$$

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

$$y-6=\log_{e}\left(8\right)$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$y=3\ln(2)-\left(-6\right)$$

Whakaoti mō y (complex solution)

$$y=3\ln(2)+6+2\pi n_{1}i$$

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