Whakaoti i te 16^x=1/64

$$16 ^ { x } = \frac { 1 } { 64 }$$

Whakaoti mō x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

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.

$$16^{x}=\frac{1}{64}$$

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

$$\log(16^{x})=\log(\frac{1}{64})$$

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

$$x\log(16)=\log(\frac{1}{64})$$

Whakawehea ngā taha e rua ki te \log(16).

$$x=\frac{\log(\frac{1}{64})}{\log(16)}$$

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

$$x=\log_{16}\left(\frac{1}{64}\right)$$

Whakaoti mō x (complex solution)

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

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