Whakaoti i te 4^x=7

$$4 ^ { x } = 7$$

Whakaoti mō x

$$x = \frac{\log_{2} {(7)}}{2} \approx 1.403677461$$

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.

$$4^{x}=7$$

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

$$\log(4^{x})=\log(7)$$

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

$$x\log(4)=\log(7)$$

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

$$x=\frac{\log(7)}{\log(4)}$$

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

$$x=\log_{4}\left(7\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(7\right)}{2}$$

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