Whakaoti i te 2^x+1+1={100001}_{2}

$${ 2 }^{ x+1 } +1 = { 100001 }_{ 2 }$$

Whakaoti mō x

$$x=5\log_{2}\left(5\right)+4\approx 15.609640474$$

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.

$$2^{x+1}+1=100001$$

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

$$2^{x+1}=100000$$

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

$$\log(2^{x+1})=\log(100000)$$

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

$$\left(x+1\right)\log(2)=\log(100000)$$

Whakawehea ngā taha e rua ki te \log(2).

$$x+1=\frac{\log(100000)}{\log(2)}$$

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

$$x+1=\log_{2}\left(100000\right)$$

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

$$x=5\log_{2}\left(10\right)-1$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+5\log_{2}\left(5\right)+4$$

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