Whakaoti i te 4^2x=100

$$4 ^ { 2 x } = 100$$

Whakaoti mō x

$$x = \frac{\log_{2} {(10)}}{2} \approx 1.660964047$$

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.

$$4^{2x}=100$$

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

$$\log(4^{2x})=\log(100)$$

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

$$2x\log(4)=\log(100)$$

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

$$2x=\frac{\log(100)}{\log(4)}$$

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

$$2x=\log_{4}\left(100\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\log_{2}\left(10\right)}{2}$$