Whakaoti i te 4^6y=9

$$4 ^ { 6 y } = 9$$

Whakaoti mō y

$$y=\frac{\log_{2}\left(3\right)}{6}\approx 0.264160417$$

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.

$$4^{6y}=9$$

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

$$\log(4^{6y})=\log(9)$$

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

$$6y\log(4)=\log(9)$$

Whakawehea ngā taha e rua ki te \log(4).

$$6y=\frac{\log(9)}{\log(4)}$$

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

$$6y=\log_{4}\left(9\right)$$

Whakawehea ngā taha e rua ki te 6.

$$y=\frac{\log_{2}\left(3\right)}{6}$$

Whakaoti mō y (complex solution)

$$y=\frac{\pi n_{1}i}{6\ln(2)}+\frac{\log_{2}\left(3\right)}{6}$$

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