Whakaoti i te 25=510(5)^x

$$25 = 510 ( 5 ) ^ { x }$$

Whakaoti mō x

$$x=-\log_{5}\left(102\right)+1\approx -1.87365718$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakawehea ngā taha e rua ki te 510.

$$\frac{25}{510}=5^{x}$$

Whakahekea te hautanga \frac{25}{510} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{5}{102}=5^{x}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$5^{x}=\frac{5}{102}$$

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

$$\log(5^{x})=\log(\frac{5}{102})$$

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

$$x\log(5)=\log(\frac{5}{102})$$

Whakawehea ngā taha e rua ki te \log(5).

$$x=\frac{\log(\frac{5}{102})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{5}{102}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(\frac{5}{102}\right)$$

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