Réitigh 20=50(92)^x

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

Réitigh do x.

$$x=\log_{92}\left(\frac{2}{5}\right)\approx -0.202639004$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 50.

$$\frac{20}{50}=92^{x}$$

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

$$\frac{2}{5}=92^{x}$$

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

$$92^{x}=\frac{2}{5}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(92^{x})=\log(\frac{2}{5})$$

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

$$x\log(92)=\log(\frac{2}{5})$$

Roinn an dá thaobh faoi \log(92).

$$x=\frac{\log(\frac{2}{5})}{\log(92)}$$

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

$$x=\log_{92}\left(\frac{2}{5}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(92)}+\log_{92}\left(\frac{2}{5}\right)$$

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