Whakaoti i te 3^-1x-1=1/9

$$3 ^ { - 1 x - 1 } = \frac { 1 } { 9 }$$

Whakaoti mō x

$$x=1$$

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.

$$3^{-x-1}=\frac{1}{9}$$

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

$$\log(3^{-x-1})=\log(\frac{1}{9})$$

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

$$\left(-x-1\right)\log(3)=\log(\frac{1}{9})$$

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

$$-x-1=\frac{\log(\frac{1}{9})}{\log(3)}$$

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

$$-x-1=\log_{3}\left(\frac{1}{9}\right)$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$-x=-2-\left(-1\right)$$

Whakawehea ngā taha e rua ki te -1.

$$x=-\frac{1}{-1}$$

Whakaoti mō x (complex solution)

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

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