Whakaoti i te 5^-x=4

$$5 ^ { - x } = 4$$

Whakaoti mō x

$$x=-2\log_{5}\left(2\right)\approx -0.861353116$$

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.

$$5^{-x}=4$$

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

$$\log(5^{-x})=\log(4)$$

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

$$-x\log(5)=\log(4)$$

Whakawehea ngā taha e rua ki te \log(5).

$$-x=\frac{\log(4)}{\log(5)}$$

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

$$-x=\log_{5}\left(4\right)$$

Whakawehea ngā taha e rua ki te -1.

$$x=\frac{2\log_{5}\left(2\right)}{-1}$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(5)}-2\log_{5}\left(2\right)$$

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