Réitigh 25=510(5)^x

$$25 = 510 ( 5 ) ^ { x }$$

Réitigh do x.

$$x=-\log_{5}\left(102\right)+1\approx -1.87365718$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 510.

$$\frac{25}{510}=5^{x}$$

Laghdaigh an codán \frac{25}{510} chuig na téarmaí is ísle trí 5 a bhaint agus a chealú.

$$\frac{5}{102}=5^{x}$$

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

$$5^{x}=\frac{5}{102}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(5^{x})=\log(\frac{5}{102})$$

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

$$x\log(5)=\log(\frac{5}{102})$$

Roinn an dá thaobh faoi \log(5).

$$x=\frac{\log(\frac{5}{102})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{5}{102}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(\frac{5}{102}\right)$$

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