Whakaoti i te 11^x=5

$$11 ^ { x } = 5$$

Whakaoti mō x

$$x=\log_{11}\left(5\right)\approx 0.671187741$$

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.

$$11^{x}=5$$

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

$$\log(11^{x})=\log(5)$$

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

$$x\log(11)=\log(5)$$

Whakawehea ngā taha e rua ki te \log(11).

$$x=\frac{\log(5)}{\log(11)}$$

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

$$x=\log_{11}\left(5\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(11)}+\log_{11}\left(5\right)$$

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