Réitigh 144489/800=103^x

$$\frac{ 144489 }{ 800 } = { 103 }^{ x }$$

Réitigh do x.

$$x=\log_{103}\left(\frac{144489}{800}\right)\approx 1.121176005$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$103^{x}=\frac{144489}{800}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(103^{x})=\log(\frac{144489}{800})$$

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

$$x\log(103)=\log(\frac{144489}{800})$$

Roinn an dá thaobh faoi \log(103).

$$x=\frac{\log(\frac{144489}{800})}{\log(103)}$$

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

$$x=\log_{103}\left(\frac{144489}{800}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(103)}+\log_{103}\left(\frac{144489}{800}\right)$$

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