Whakaoti i te -6*2^0.1x=-100

$$- 6 \cdot 2 ^ { 0.1 x } = - 100$$

Whakaoti mō x

$$x=\log_{2}\left(\frac{95367431640625}{59049}\right)+10\approx 40.588936891$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakawehea ngā taha e rua ki te -6.

$$2^{0.1x}=\frac{-100}{-6}$$

Whakahekea te hautanga \frac{-100}{-6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -2.

$$2^{0.1x}=\frac{50}{3}$$

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

$$\log(2^{0.1x})=\log(\frac{50}{3})$$

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

$$0.1x\log(2)=\log(\frac{50}{3})$$

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

$$0.1x=\frac{\log(\frac{50}{3})}{\log(2)}$$

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

$$0.1x=\log_{2}\left(\frac{50}{3}\right)$$

Me whakarea ngā taha e rua ki te 10.

$$x=\frac{\ln(\frac{50}{3})}{0.1\ln(2)}$$

Whakaoti mō x (complex solution)

$$x=\frac{i\times 20\pi n_{1}}{\ln(2)}+\log_{2}\left(\frac{95367431640625}{59049}\right)+10$$

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