Whakaoti i te =16*(1/4)^2x=32

$$= 16 \cdot ( \frac { 1 } { 4 } ) ^ { 2 x } = 32$$

Whakaoti mō x

$$x=-\frac{1}{4}=-0.25$$

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.

$$16\times \left(\frac{1}{4}\right)^{2x}=32$$

Whakawehea ngā taha e rua ki te 16.

$$\left(\frac{1}{4}\right)^{2x}=2$$

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

$$\log(\left(\frac{1}{4}\right)^{2x})=\log(2)$$

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

$$2x\log(\frac{1}{4})=\log(2)$$

Whakawehea ngā taha e rua ki te \log(\frac{1}{4}).

$$2x=\frac{\log(2)}{\log(\frac{1}{4})}$$

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

$$2x=\log_{\frac{1}{4}}\left(2\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=-\frac{\frac{1}{2}}{2}$$

Whakaoti mō x (complex solution)

$$x=-\frac{\pi n_{1}i}{2\ln(2)}-\frac{1}{4}$$

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