Réitigh -6*2^0.1x=-100

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

Réitigh do x.

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

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi -6.

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

Laghdaigh an codán \frac{-100}{-6} chuig na téarmaí is ísle trí -2 a bhaint agus a chealú.

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

Ghlac logartam an dá thaobh den chothromóid.

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

Is ionann logartam uimhreacha a ardaítear go cumhacht agus an chumhacht méadaithe faoi logartam na huimhreach.

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

Roinn an dá thaobh faoi \log(2).

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

Leis an bhfoirmle athrú boinn \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

Iolraigh an dá thaobh faoi 10.

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

Réitigh do x. (complex solution)

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

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