Whakaoti i te 180434=10225^4x

$$180434= { 10225 }^{ 4x }$$

Whakaoti mō x

$$x=\frac{\log_{10225}\left(180434\right)}{4}\approx 0.327728163$$

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

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

$$10225^{4x}=180434$$

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

$$\log(10225^{4x})=\log(180434)$$

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

$$4x\log(10225)=\log(180434)$$

Whakawehea ngā taha e rua ki te \log(10225).

$$4x=\frac{\log(180434)}{\log(10225)}$$

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

$$4x=\log_{10225}\left(180434\right)$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{\log_{10225}\left(180434\right)}{4}$$

Whakaoti mō x (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(10225)}+\frac{\log_{10225}\left(180434\right)}{4}$$

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