Whakaoti i te (2/5)^x=125/8

$$( \frac { 2 } { 5 } ) ^ { x } = \frac { 125 } { 8 }$$

Whakaoti mō x

$$x=-3$$

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.

$$\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$$

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

$$\log(\left(\frac{2}{5}\right)^{x})=\log(\frac{125}{8})$$

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

$$x\log(\frac{2}{5})=\log(\frac{125}{8})$$

Whakawehea ngā taha e rua ki te \log(\frac{2}{5}).

$$x=\frac{\log(\frac{125}{8})}{\log(\frac{2}{5})}$$

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

$$x=\log_{\frac{2}{5}}\left(\frac{125}{8}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{2}{5})}+\log_{\frac{2}{5}}\left(\frac{125}{8}\right)$$

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