Whakaoti i te 4^-x=37

$$4 ^ { - x } = 37$$

Whakaoti mō x

$$x = -\frac{\log_{2} {(37)}}{2} \approx -2.604726683$$

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.

$$4^{-x}=37$$

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

$$\log(4^{-x})=\log(37)$$

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

$$-x\log(4)=\log(37)$$

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

$$-x=\frac{\log(37)}{\log(4)}$$

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

$$-x=\log_{4}\left(37\right)$$

Whakawehea ngā taha e rua ki te -1.

$$x=\frac{\log_{2}\left(37\right)}{-2}$$

Whakaoti mō x (complex solution)

$$x=-\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(37\right)}{2}$$

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