Whakaoti i te (33^7)^4/3^3=3^5*x

$$\frac { ( 33 ^ { 7 } ) ^ { 4 } } { 3 ^ { 3 } } = 3 ^ { 5 \cdot x }$$

Whakaoti mō x

$$x=\frac{28\log_{3}\left(11\right)}{5}+5\approx 17.222886696$$

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 7 me te 4 kia riro ai te 28.

$$\frac{33^{28}}{3^{3}}=3^{5x}$$

Tātaihia te 33 mā te pū o 28, kia riro ko 3299060778251569566188233498374847942355841.

$$\frac{3299060778251569566188233498374847942355841}{3^{3}}=3^{5x}$$

Tātaihia te 3 mā te pū o 3, kia riro ko 27.

$$\frac{3299060778251569566188233498374847942355841}{27}=3^{5x}$$

Whakawehea te 3299060778251569566188233498374847942355841 ki te 27, kia riro ko 122187436231539613562527166606475849716883.

$$122187436231539613562527166606475849716883=3^{5x}$$

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

$$3^{5x}=122187436231539613562527166606475849716883$$

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

$$\log(3^{5x})=\log(122187436231539613562527166606475849716883)$$

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

$$5x\log(3)=\log(122187436231539613562527166606475849716883)$$

Whakawehea ngā taha e rua ki te \log(3).

$$5x=\frac{\log(122187436231539613562527166606475849716883)}{\log(3)}$$

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

$$5x=\log_{3}\left(122187436231539613562527166606475849716883\right)$$

Whakawehea ngā taha e rua ki te 5.

$$x=\frac{\log_{3}\left(122187436231539613562527166606475849716883\right)}{5}$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(3)}+\frac{28\log_{3}\left(11\right)}{5}+5$$

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