Whakaoti i te 47^xdiv47^21=47^45

$$47 ^ { x } \div 47 ^ { 21 } = 47 ^ { 45 }$$

Whakaoti mō x

$$x=66$$

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.

$$\frac{1}{130033429462229783044185156533092847}\times 47^{x}=1755511210260049172778020908173078657717675374080672665297567056535308458607$$

Me whakarea ngā taha e rua ki te 130033429462229783044185156533092847.

$$47^{x}=228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129$$

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

$$\log(47^{x})=\log(228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129)$$

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

$$x\log(47)=\log(228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129)$$

Whakawehea ngā taha e rua ki te \log(47).

$$x=\frac{\log(228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129)}{\log(47)}$$

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

$$x=\log_{47}\left(228275143129503741495076954846893197188864748274459173176003261052016035107201719695009640374487379913987284129\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(47)}+66$$

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