Whakaoti i te 6^-3x=4

$$6 ^ { - 3 x } = 4$$

Whakaoti mō x

$$x=-\frac{2\log_{6}\left(2\right)}{3}\approx -0.257901871$$

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.

$$6^{-3x}=4$$

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

$$\log(6^{-3x})=\log(4)$$

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

$$-3x\log(6)=\log(4)$$

Whakawehea ngā taha e rua ki te \log(6).

$$-3x=\frac{\log(4)}{\log(6)}$$

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

$$-3x=\log_{6}\left(4\right)$$

Whakawehea ngā taha e rua ki te -3.

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

Whakaoti mō x (complex solution)

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

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