Whakaoti i te 3^x=1/6

$$3 ^ { x } = \frac { 1 } { 6 }$$

Whakaoti mō x

$$x=-\log_{3}\left(6\right)\approx -1.630929754$$

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.

$$3^{x}=\frac{1}{6}$$

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

$$\log(3^{x})=\log(\frac{1}{6})$$

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

$$x\log(3)=\log(\frac{1}{6})$$

Whakawehea ngā taha e rua ki te \log(3).

$$x=\frac{\log(\frac{1}{6})}{\log(3)}$$

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

$$x=\log_{3}\left(\frac{1}{6}\right)$$

Whakaoti mō x (complex solution)

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

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