Whakaoti i te e^frac{x{4}}=205

$$e ^ { \frac { x } { 4 } } = 205$$

Whakaoti mō x

$$x=4\ln(205)\approx 21.292039917$$

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.

$$e^{\frac{1}{4}x}=205$$

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

$$\log(e^{\frac{1}{4}x})=\log(205)$$

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

$$\frac{1}{4}x\log(e)=\log(205)$$

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

$$\frac{1}{4}x=\frac{\log(205)}{\log(e)}$$

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

$$\frac{1}{4}x=\log_{e}\left(205\right)$$

Me whakarea ngā taha e rua ki te 4.

$$x=\frac{\ln(205)}{\frac{1}{4}}$$

Whakaoti mō x (complex solution)

$$x=4\ln(205)+i\times 8\pi n_{1}$$

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