Whakaoti i te 5^-5x=8

$$5 ^ { - 5 x } = 8$$

Whakaoti mō x

$$x=-\frac{3\log_{5}\left(2\right)}{5}\approx -0.258405935$$

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.

$$5^{-5x}=8$$

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

$$\log(5^{-5x})=\log(8)$$

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

$$-5x\log(5)=\log(8)$$

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

$$-5x=\frac{\log(8)}{\log(5)}$$

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

$$-5x=\log_{5}\left(8\right)$$

Whakawehea ngā taha e rua ki te -5.

$$x=\frac{3\log_{5}\left(2\right)}{-5}$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\pi n_{1}i}{5\ln(5)}-\frac{3\log_{5}\left(2\right)}{5}$$

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