Réitigh 20=50(.92)^x

$$20 = 50 ( .92 ) ^ { x }$$

Réitigh do x.

$$x=\log_{0.92}\left(0.4\right)\approx 10.989122704$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 50.

$$\frac{20}{50}=0.92^{x}$$

Laghdaigh an codán \frac{20}{50} chuig na téarmaí is ísle trí 10 a bhaint agus a chealú.

$$\frac{2}{5}=0.92^{x}$$

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

$$0.92^{x}=\frac{2}{5}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(0.92^{x})=\log(\frac{2}{5})$$

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

$$x\log(0.92)=\log(\frac{2}{5})$$

Roinn an dá thaobh faoi \log(0.92).

$$x=\frac{\log(\frac{2}{5})}{\log(0.92)}$$

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

$$x=\log_{0.92}\left(\frac{2}{5}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.92)}+\log_{0.92}\left(0.4\right)$$

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