Whakaoti i te 6^x=1/216

$$6 ^ { x } = \frac { 1 } { 216 }$$

Whakaoti mō x

$$x=-3$$

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.

$$6^{x}=\frac{1}{216}$$

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

$$\log(6^{x})=\log(\frac{1}{216})$$

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

$$x\log(6)=\log(\frac{1}{216})$$

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

$$x=\frac{\log(\frac{1}{216})}{\log(6)}$$

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

$$x=\log_{6}\left(\frac{1}{216}\right)$$

Whakaoti mō x (complex solution)

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

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