Whakaoti i te 47=610(0.5)^frac{x{4}}

$$47 = 610 ( 0.5 ) ^ { \frac { x } { 4 } }$$

Whakaoti mō x

$$x=4\log_{2}\left(\frac{610}{47}\right)\approx 14.792306323$$

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

Whakawehea ngā taha e rua ki te 610.

$$\frac{47}{610}=0.5^{\frac{x}{4}}$$

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

$$0.5^{\frac{x}{4}}=\frac{47}{610}$$

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$0.5^{\frac{1}{4}x}=\frac{47}{610}$$

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

$$\log(0.5^{\frac{1}{4}x})=\log(\frac{47}{610})$$

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

$$\frac{1}{4}x\log(0.5)=\log(\frac{47}{610})$$

Whakawehea ngā taha e rua ki te \log(0.5).

$$\frac{1}{4}x=\frac{\log(\frac{47}{610})}{\log(0.5)}$$

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

$$\frac{1}{4}x=\log_{0.5}\left(\frac{47}{610}\right)$$

Me whakarea ngā taha e rua ki te 4.

$$x=-\frac{\frac{\ln(\frac{47}{610})}{\ln(2)}}{\frac{1}{4}}$$

Whakaoti mō x (complex solution)

$$x=-\frac{i\times 8\pi n_{1}}{\ln(2)}+4\log_{2}\left(\frac{610}{47}\right)$$

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