Whakaoti i te 4^x-1=16

$$4 ^ { x - 1 } = 16$$

Whakaoti mō x

$$x=3$$

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.

$$4^{x-1}=16$$

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

$$\log(4^{x-1})=\log(16)$$

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

$$\left(x-1\right)\log(4)=\log(16)$$

Whakawehea ngā taha e rua ki te \log(4).

$$x-1=\frac{\log(16)}{\log(4)}$$

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

$$x-1=\log_{4}\left(16\right)$$

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

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

Whakaoti mō x (complex solution)

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

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