Réitigh 4div10=2^x

$$4 \div 10 = { 2 }^{ x }$$

Réitigh do x.

$$x=-\log_{2}\left(5\right)+1\approx -1.321928095$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Laghdaigh an codán \frac{4}{10} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$\frac{2}{5}=2^{x}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$2^{x}=\frac{2}{5}$$

Ghlac logartam an dá thaobh den chothromóid.

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

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

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

Roinn an dá thaobh faoi \log(2).

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

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

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

Réitigh do x. (complex solution)

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

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