Whakaoti i te 4^-x=3.7

$$4 ^ { - x } = 3.7$$

Whakaoti mō x

$$x=\frac{\log_{2}\left(\frac{10}{37}\right)}{2}\approx -0.943762635$$

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.

$$4^{-x}=3.7$$

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

$$\log(4^{-x})=\log(3.7)$$

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

$$-x\log(4)=\log(3.7)$$

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

$$-x=\frac{\log(3.7)}{\log(4)}$$

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

$$-x=\log_{4}\left(3.7\right)$$

Whakawehea ngā taha e rua ki te -1.

$$x=\frac{\ln(\frac{37}{10})}{-2\ln(2)}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\pi n_{1}}{\ln(2)}+\frac{\log_{2}\left(\frac{10}{37}\right)}{2}$$

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