Whakaoti i te 3(13^x)=5

$$3 ( 13 ^ { x } ) = 5$$

Whakaoti mō x

$$x=\log_{13}\left(\frac{5}{3}\right)\approx 0.199156222$$

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.

$$3\times 13^{x}=5$$

Whakawehea ngā taha e rua ki te 3.

$$13^{x}=\frac{5}{3}$$

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

$$\log(13^{x})=\log(\frac{5}{3})$$

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

$$x\log(13)=\log(\frac{5}{3})$$

Whakawehea ngā taha e rua ki te \log(13).

$$x=\frac{\log(\frac{5}{3})}{\log(13)}$$

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

$$x=\log_{13}\left(\frac{5}{3}\right)$$

Whakaoti mō x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(13)}+\log_{13}\left(\frac{5}{3}\right)$$

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