Whakaoti i te 2^-2x=8

$$2 ^ { - 2 x } = 8$$

Whakaoti mō x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

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.

$$2^{-2x}=8$$

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

$$\log(2^{-2x})=\log(8)$$

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

$$-2x\log(2)=\log(8)$$

Whakawehea ngā taha e rua ki te \log(2).

$$-2x=\frac{\log(8)}{\log(2)}$$

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

$$-2x=\log_{2}\left(8\right)$$

Whakawehea ngā taha e rua ki te -2.

$$x=\frac{3}{-2}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\pi n_{1}}{\ln(2)}-\frac{3}{2}$$

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