Whakaoti i te 6*2^frac{x{4}}=222

$$6 \cdot 2 ^ { \frac { x } { 4 } } = 222$$

Whakaoti mō x

$$x=4\log_{2}\left(37\right)\approx 20.837813463$$

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.

$$6\times 2^{\frac{1}{4}x}=222$$

Whakawehea ngā taha e rua ki te 6.

$$2^{\frac{1}{4}x}=37$$

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

$$\log(2^{\frac{1}{4}x})=\log(37)$$

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

$$\frac{1}{4}x\log(2)=\log(37)$$

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

$$\frac{1}{4}x=\frac{\log(37)}{\log(2)}$$

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

$$\frac{1}{4}x=\log_{2}\left(37\right)$$

Me whakarea ngā taha e rua ki te 4.

$$x=\frac{\log_{2}\left(37\right)}{\frac{1}{4}}$$

Whakaoti mō x (complex solution)

$$x=\frac{8\pi n_{1}i}{\ln(2)}+4\log_{2}\left(37\right)$$

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