Whakaoti i te 2^-x=3/2

$$2 ^ { - x } = \frac { 3 } { 2 }$$

Whakaoti mō x

$$x=-\log_{2}\left(3\right)+1\approx -0.584962501$$

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.

$$2^{-x}=\frac{3}{2}$$

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

$$\log(2^{-x})=\log(\frac{3}{2})$$

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

$$-x\log(2)=\log(\frac{3}{2})$$

Whakawehea ngā taha e rua ki te \log(2).

$$-x=\frac{\log(\frac{3}{2})}{\log(2)}$$

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

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

Whakawehea ngā taha e rua ki te -1.

$$x=\frac{\log_{2}\left(3\right)-1}{-1}$$

Whakaoti mō x (complex solution)

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

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