Réitigh 47000000div9428=123^x

$$47000000 \div 9428 = { 123 }^{ x }$$

Réitigh do x.

$$x=\log_{123}\left(\frac{11750000}{2357}\right)\approx 1.769304388$$

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.

$$\frac{11750000}{2357}=123^{x}$$

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

$$123^{x}=\frac{11750000}{2357}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(123^{x})=\log(\frac{11750000}{2357})$$

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

$$x\log(123)=\log(\frac{11750000}{2357})$$

Roinn an dá thaobh faoi \log(123).

$$x=\frac{\log(\frac{11750000}{2357})}{\log(123)}$$

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

$$x=\log_{123}\left(\frac{11750000}{2357}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(\frac{11750000}{2357}\right)$$

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