Whakaoti i te 20^-x=1/7

$${ 20 }^{ -x } = \frac{ 1 }{ 7 }$$

Whakaoti mō x

$$x=\log_{20}\left(7\right)\approx 0.649560766$$

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.

$$20^{-x}=\frac{1}{7}$$

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

$$\log(20^{-x})=\log(\frac{1}{7})$$

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

$$-x\log(20)=\log(\frac{1}{7})$$

Whakawehea ngā taha e rua ki te \log(20).

$$-x=\frac{\log(\frac{1}{7})}{\log(20)}$$

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

$$-x=\log_{20}\left(\frac{1}{7}\right)$$

Whakawehea ngā taha e rua ki te -1.

$$x=-\frac{\log_{20}\left(7\right)}{-1}$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(20)}+\log_{20}\left(7\right)$$

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