Whakaoti i te 7(1/3)^x=63

$$7 ( \frac { 1 } { 3 } ) ^ { x } = 63$$

Whakaoti mō x

$$x=-2$$

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.

$$7\times \left(\frac{1}{3}\right)^{x}=63$$

Whakawehea ngā taha e rua ki te 7.

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

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

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

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

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

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

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

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

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

Whakaoti mō x (complex solution)

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

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