Whakaoti i te 2^2x+7=2^15

$$2 ^ { 2 x + 7 } = 2 ^ { 15 }$$

Whakaoti mō x

$$x=4$$

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.

$$2^{2x+7}=32768$$

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

$$\log(2^{2x+7})=\log(32768)$$

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

$$\left(2x+7\right)\log(2)=\log(32768)$$

Whakawehea ngā taha e rua ki te \log(2).

$$2x+7=\frac{\log(32768)}{\log(2)}$$

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

$$2x+7=\log_{2}\left(32768\right)$$

Me tango 7 mai i ngā taha e rua o te whārite.

$$2x=15-7$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{8}{2}$$

Whakaoti mō x (complex solution)

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

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