Whakaoti i te 391^12=2^x

$${ 391 }^{ 12 } = { 2 }^{ x }$$

Whakaoti mō x

$$x=12\log_{2}\left(391\right)\approx 103.332297568$$

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

Tātaihia te 391 mā te pū o 12, kia riro ko 12767947514633659874603497973281.

$$12767947514633659874603497973281=2^{x}$$

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

$$2^{x}=12767947514633659874603497973281$$

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

$$\log(2^{x})=\log(12767947514633659874603497973281)$$

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

$$x\log(2)=\log(12767947514633659874603497973281)$$

Whakawehea ngā taha e rua ki te \log(2).

$$x=\frac{\log(12767947514633659874603497973281)}{\log(2)}$$

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

$$x=\log_{2}\left(12767947514633659874603497973281\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+12\log_{2}\left(391\right)$$

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