Réitigh 180434=10225^4x

$$180434= { 10225 }^{ 4x }$$

Réitigh do x.

$$x=\frac{\log_{10225}\left(180434\right)}{4}\approx 0.327728163$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$10225^{4x}=180434$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(10225^{4x})=\log(180434)$$

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

$$4x\log(10225)=\log(180434)$$

Roinn an dá thaobh faoi \log(10225).

$$4x=\frac{\log(180434)}{\log(10225)}$$

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

$$4x=\log_{10225}\left(180434\right)$$

Roinn an dá thaobh faoi 4.

$$x=\frac{\log_{10225}\left(180434\right)}{4}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{2\ln(10225)}+\frac{\log_{10225}\left(180434\right)}{4}$$

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