Whakaoti i te frac{5^{m}*5^3*5^-2}{5^-3}=5^1

$$\frac { 5 ^ { m } \times 5 ^ { 3 } \times 5 ^ { - 2 } } { 5 ^ { - 3 } } = 5 ^ { 1 }$$

Whakaoti mō m

$$m=-3$$

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

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 3 me te -2 kia riro ai te 1.

$$\frac{5^{m}\times 5^{1}}{5^{-3}}=5^{1}$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

$$5^{4}\times 5^{m}=5^{1}$$

Tātaihia te 5 mā te pū o 1, kia riro ko 5.

$$5^{4}\times 5^{m}=5$$

Tātaihia te 5 mā te pū o 4, kia riro ko 625.

$$625\times 5^{m}=5$$

Whakawehea ngā taha e rua ki te 625.

$$5^{m}=\frac{5}{625}$$

Whakahekea te hautanga \frac{5}{625} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$5^{m}=\frac{1}{125}$$

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

$$\log(5^{m})=\log(\frac{1}{125})$$

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

$$m\log(5)=\log(\frac{1}{125})$$

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

$$m=\frac{\log(\frac{1}{125})}{\log(5)}$$

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

$$m=\log_{5}\left(\frac{1}{125}\right)$$