Whakaoti i te 2^-3x=64

$$2 ^ { - 3 x } = 64$$

Whakaoti mō x

$$x=-2$$

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.

$$2^{-3x}=64$$

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

$$\log(2^{-3x})=\log(64)$$

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

$$-3x\log(2)=\log(64)$$

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

$$-3x=\frac{\log(64)}{\log(2)}$$

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

$$-3x=\log_{2}\left(64\right)$$

Whakawehea ngā taha e rua ki te -3.

$$x=\frac{6}{-3}$$

Whakaoti mō x (complex solution)

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

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