Whakaoti i te 4^2x-3div4^4=64

$$4 ^ { 2 x - 3 } \div 4 ^ { 4 } = 64$$

Whakaoti mō x

$$x=5$$

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.

$$\frac{1}{256}\times 4^{2x-3}=64$$

Me whakarea ngā taha e rua ki te 256.

$$4^{2x-3}=16384$$

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

$$\log(4^{2x-3})=\log(16384)$$

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

$$\left(2x-3\right)\log(4)=\log(16384)$$

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

$$2x-3=\frac{\log(16384)}{\log(4)}$$

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

$$2x-3=\log_{4}\left(16384\right)$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$2x=7-\left(-3\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{10}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(2)}+5$$

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