Whakaoti i te (100)(102^2x)=500000

$$(100)( { 102 }^{ 2x } )=500000$$

Whakaoti mō x

$$x=\frac{\log_{102}\left(5000\right)}{2}\approx 0.920783055$$

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.

$$100\times 102^{2x}=500000$$

Whakawehea ngā taha e rua ki te 100.

$$102^{2x}=5000$$

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

$$\log(102^{2x})=\log(5000)$$

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

$$2x\log(102)=\log(5000)$$

Whakawehea ngā taha e rua ki te \log(102).

$$2x=\frac{\log(5000)}{\log(102)}$$

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

$$2x=\log_{102}\left(5000\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=\frac{\log_{102}\left(5000\right)}{2}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(102)}+\frac{\log_{102}\left(5000\right)}{2}$$

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