Whakaoti i te 0.99^x=0.45

$${ 0.99 }^{ x } =0.45$$

Whakaoti mō x

$$x=\log_{0.99}\left(0.45\right)\approx 79.450847002$$

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.

$$0.99^{x}=0.45$$

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

$$\log(0.99^{x})=\log(0.45)$$

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

$$x\log(0.99)=\log(0.45)$$

Whakawehea ngā taha e rua ki te \log(0.99).

$$x=\frac{\log(0.45)}{\log(0.99)}$$

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

$$x=\log_{0.99}\left(0.45\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.99)}+\log_{0.99}\left(0.45\right)$$

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