Whakaoti i te 138*2^2x=46

$$138 \cdot 2 ^ { 2 x } = 46$$

Whakaoti mō x

$$x=-\frac{\log_{2}\left(3\right)}{2}\approx -0.79248125$$

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.

$$138\times 2^{2x}=46$$

Whakawehea ngā taha e rua ki te 138.

$$2^{2x}=\frac{1}{3}$$

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

$$\log(2^{2x})=\log(\frac{1}{3})$$

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

$$2x\log(2)=\log(\frac{1}{3})$$

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

$$2x=\frac{\log(\frac{1}{3})}{\log(2)}$$

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

$$2x=\log_{2}\left(\frac{1}{3}\right)$$

Whakawehea ngā taha e rua ki te 2.

$$x=-\frac{\log_{2}\left(3\right)}{2}$$

Whakaoti mō x (complex solution)

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

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