Whakaoti i te 2^x+2^x=2^18

$${ 2 }^{ x } + { 2 }^{ x } = { 2 }^{ 18 }$$

Whakaoti mō x

$$x=17$$

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

Pahekotia te 2^{x} me 2^{x}, ka 2\times 2^{x}.

$$2\times 2^{x}=2^{18}$$

Tātaihia te 2 mā te pū o 18, kia riro ko 262144.

$$2\times 2^{x}=262144$$

Whakawehea ngā taha e rua ki te 2.

$$2^{x}=\frac{262144}{2}$$

Whakawehea te 262144 ki te 2, kia riro ko 131072.

$$2^{x}=131072$$

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

$$\log(2^{x})=\log(131072)$$

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

$$x\log(2)=\log(131072)$$

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

$$x=\frac{\log(131072)}{\log(2)}$$

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

$$x=\log_{2}\left(131072\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+17$$

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