Whakaoti i te 37=8^x+3

$$37 = 8 ^ { x + 3 }$$

Whakaoti mō x

$$x=\frac{\log_{2}\left(37\right)-9}{3}\approx -1.263515545$$

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.

$$8^{x+3}=37$$

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

$$\log(8^{x+3})=\log(37)$$

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

$$\left(x+3\right)\log(8)=\log(37)$$

Whakawehea ngā taha e rua ki te \log(8).

$$x+3=\frac{\log(37)}{\log(8)}$$

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

$$x+3=\log_{8}\left(37\right)$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$x=\frac{\log_{2}\left(37\right)}{3}-3$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{\log_{2}\left(37\right)}{3}-3$$

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