Whakaoti i te (2/7)^-3*(2/7)^-11=(2/7)^x

$$( \frac { 2 } { 7 } ) ^ { - 3 } \times ( \frac { 2 } { 7 } ) ^ { - 11 } = ( \frac { 2 } { 7 } ) ^ { x }$$

Whakaoti mō x

$$x=-14$$

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 -11 kia riro ai te -14.

$$\left(\frac{2}{7}\right)^{-14}=\left(\frac{2}{7}\right)^{x}$$

Tātaihia te \frac{2}{7} mā te pū o -14, kia riro ko \frac{678223072849}{16384}.

$$\frac{678223072849}{16384}=\left(\frac{2}{7}\right)^{x}$$

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

$$\left(\frac{2}{7}\right)^{x}=\frac{678223072849}{16384}$$

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

$$\log(\left(\frac{2}{7}\right)^{x})=\log(\frac{678223072849}{16384})$$

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

$$x\log(\frac{2}{7})=\log(\frac{678223072849}{16384})$$

Whakawehea ngā taha e rua ki te \log(\frac{2}{7}).

$$x=\frac{\log(\frac{678223072849}{16384})}{\log(\frac{2}{7})}$$

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

$$x=\log_{\frac{2}{7}}\left(\frac{678223072849}{16384}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{2}{7})}+2\log_{\frac{2}{7}}\left(\frac{823543}{128}\right)$$

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