Whakaoti i te 32^x+1=24

$$32 ^ { x + 1 } = 24$$

Whakaoti mō x

$$x=\frac{\log_{2}\left(3\right)-2}{5}\approx -0.0830075$$

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.

$$32^{x+1}=24$$

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

$$\log(32^{x+1})=\log(24)$$

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

$$\left(x+1\right)\log(32)=\log(24)$$

Whakawehea ngā taha e rua ki te \log(32).

$$x+1=\frac{\log(24)}{\log(32)}$$

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

$$x+1=\log_{32}\left(24\right)$$

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

$$x=\frac{\log_{2}\left(24\right)}{5}-1$$

Whakaoti mō x (complex solution)

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

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