Réitigh 8000=4500(1024)^x

$$8000 = 4500 ( 1024 ) ^ { x }$$

Réitigh do x.

$$x=\frac{-\log_{2}\left(3\right)+2}{5}\approx 0.0830075$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 4500.

$$\frac{8000}{4500}=1024^{x}$$

Laghdaigh an codán \frac{8000}{4500} chuig na téarmaí is ísle trí 500 a bhaint agus a chealú.

$$\frac{16}{9}=1024^{x}$$

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

$$1024^{x}=\frac{16}{9}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1024^{x})=\log(\frac{16}{9})$$

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

$$x\log(1024)=\log(\frac{16}{9})$$

Roinn an dá thaobh faoi \log(1024).

$$x=\frac{\log(\frac{16}{9})}{\log(1024)}$$

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

$$x=\log_{1024}\left(\frac{16}{9}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{5\ln(2)}-\frac{\log_{2}\left(3\right)}{5}+\frac{2}{5}$$

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