Whakaoti i te 3^x+1=(273/10)^4

$$3 ^ { x + 1 } = ( \frac { 273 } { 10 } ) ^ { 4 }$$

Whakaoti mō x

$$x=\log_{3}\left(\frac{68574961}{10000}\right)+3\approx 11.040231977$$

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

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

$$3^{x+1}=\frac{5554571841}{10000}$$

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

$$\log(3^{x+1})=\log(\frac{5554571841}{10000})$$

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

$$\left(x+1\right)\log(3)=\log(\frac{5554571841}{10000})$$

Whakawehea ngā taha e rua ki te \log(3).

$$x+1=\frac{\log(\frac{5554571841}{10000})}{\log(3)}$$

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

$$x+1=\log_{3}\left(\frac{5554571841}{10000}\right)$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=\frac{\ln(\frac{5554571841}{10000})}{\ln(3)}-1$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(\frac{68574961}{10000}\right)+3$$

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