Whakaoti i te 12(2^x-5)=500

$$12 ( 2 ^ { x - 5 } ) = 500$$

Whakaoti mō x

$$x=\log_{2}\left(\frac{125}{3}\right)+5\approx 10.380821784$$

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.

$$12\times 2^{x-5}=500$$

Whakawehea ngā taha e rua ki te 12.

$$2^{x-5}=\frac{125}{3}$$

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

$$\log(2^{x-5})=\log(\frac{125}{3})$$

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

$$\left(x-5\right)\log(2)=\log(\frac{125}{3})$$

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

$$x-5=\frac{\log(\frac{125}{3})}{\log(2)}$$

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

$$x-5=\log_{2}\left(\frac{125}{3}\right)$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x=\frac{\ln(\frac{125}{3})}{\ln(2)}-\left(-5\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+\log_{2}\left(\frac{125}{3}\right)+5$$

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