Whakaoti i te e^frac{x{4}}=20.5

$$e ^ { \frac { x } { 4 } } = 20.5$$

Whakaoti mō x

$$x=\ln(176610.0625)\approx 12.081699545$$

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.

$$e^{\frac{1}{4}x}=20.5$$

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

$$\log(e^{\frac{1}{4}x})=\log(20.5)$$

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

$$\frac{1}{4}x\log(e)=\log(20.5)$$

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

$$\frac{1}{4}x=\frac{\log(20.5)}{\log(e)}$$

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

$$\frac{1}{4}x=\log_{e}\left(20.5\right)$$

Me whakarea ngā taha e rua ki te 4.

$$x=\frac{\ln(\frac{41}{2})}{\frac{1}{4}}$$

Whakaoti mō x (complex solution)

$$x=\ln(176610.0625)+i\times 8\pi n_{1}$$

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