Whakaoti i te 22(1/3)^x-7=22

$$22 ( 1 / 3 ) ^ { x - 7 } = 22$$

Whakaoti mō x

$$x=7$$

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.

$$22\times \left(\frac{1}{3}\right)^{x-7}=22$$

Whakawehea ngā taha e rua ki te 22.

$$\left(\frac{1}{3}\right)^{x-7}=1$$

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

$$\log(\left(\frac{1}{3}\right)^{x-7})=\log(1)$$

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

$$\left(x-7\right)\log(\frac{1}{3})=\log(1)$$

Whakawehea ngā taha e rua ki te \log(\frac{1}{3}).

$$x-7=\frac{\log(1)}{\log(\frac{1}{3})}$$

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

$$x-7=\log_{\frac{1}{3}}\left(1\right)$$

Me tāpiri 7 ki ngā taha e rua o te whārite.

$$x=-\left(-7\right)$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(3)}+7$$

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