Whakaoti i te 76=7^x+2

$$76 = 7 ^ { x } + 2$$

Whakaoti mō x

$$x=\log_{7}\left(74\right)\approx 2.211851917$$

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.

$$7^{x}+2=76$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$7^{x}=74$$

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

$$\log(7^{x})=\log(74)$$

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

$$x\log(7)=\log(74)$$

Whakawehea ngā taha e rua ki te \log(7).

$$x=\frac{\log(74)}{\log(7)}$$

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

$$x=\log_{7}\left(74\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(7)}+\log_{7}\left(74\right)$$

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