Whakaoti i te 4^2x+3=1

$$4 ^ { 2 x + 3 } = 1$$

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.

$$4^{2x+3}=1$$

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

$$\log(4^{2x+3})=\log(1)$$

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

$$\left(2x+3\right)\log(4)=\log(1)$$

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

$$2x+3=\frac{\log(1)}{\log(4)}$$

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

$$2x+3=\log_{4}\left(1\right)$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$2x=-3$$

Whakawehea ngā taha e rua ki te 2.

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

Whakaoti mō x (complex solution)

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

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