Réitigh 47000000div9428=1.23^x

$$47000000 \div 9428 = { 1.23 }^{ x }$$

Réitigh do x.

$$x=\log_{1.23}\left(\frac{11750000}{2357}\right)\approx 41.128676945$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Laghdaigh an codán \frac{47000000}{9428} chuig na téarmaí is ísle trí 4 a bhaint agus a chealú.

$$\frac{11750000}{2357}=1.23^{x}$$

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

$$1.23^{x}=\frac{11750000}{2357}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1.23^{x})=\log(\frac{11750000}{2357})$$

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

$$x\log(1.23)=\log(\frac{11750000}{2357})$$

Roinn an dá thaobh faoi \log(1.23).

$$x=\frac{\log(\frac{11750000}{2357})}{\log(1.23)}$$

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

$$x=\log_{1.23}\left(\frac{11750000}{2357}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.23)}+\log_{1.23}\left(\frac{11750000}{2357}\right)$$

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