Whakaoti i te (1/2)^x=1/32

$$( \frac { 1 } { 2 } ) ^ { x } = \frac { 1 } { 32 }$$

Whakaoti mō x

$$x=5$$

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.

$$\left(\frac{1}{2}\right)^{x}=\frac{1}{32}$$

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

$$\log(\left(\frac{1}{2}\right)^{x})=\log(\frac{1}{32})$$

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

$$x\log(\frac{1}{2})=\log(\frac{1}{32})$$

Whakawehea ngā taha e rua ki te \log(\frac{1}{2}).

$$x=\frac{\log(\frac{1}{32})}{\log(\frac{1}{2})}$$

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

$$x=\log_{\frac{1}{2}}\left(\frac{1}{32}\right)$$

Whakaoti mō x (complex solution)

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

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