Whakaoti i te 5^x=3

$${ 5 }^{ x } =3$$

Whakaoti mō x

$$x=\log_{5}\left(3\right)\approx 0.682606194$$

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.

$$5^{x}=3$$

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

$$\log(5^{x})=\log(3)$$

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

$$x\log(5)=\log(3)$$

Whakawehea ngā taha e rua ki te \log(5).

$$x=\frac{\log(3)}{\log(5)}$$

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

$$x=\log_{5}\left(3\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(3\right)$$

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