Whakaoti i te 1/5e^6x=4

$$\frac { 1 } { 5 } e ^ { 6 x } = 4$$

Whakaoti mō x

$$x=\frac{\ln(20)}{6}\approx 0.499288712$$

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.

$$\frac{1}{5}e^{6x}=4$$

Me whakarea ngā taha e rua ki te 5.

$$e^{6x}=20$$

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

$$\log(e^{6x})=\log(20)$$

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

$$6x\log(e)=\log(20)$$

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

$$6x=\frac{\log(20)}{\log(e)}$$

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

$$6x=\log_{e}\left(20\right)$$

Whakawehea ngā taha e rua ki te 6.

$$x=\frac{\ln(20)}{6}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{3}+\frac{\ln(20)}{6}$$

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