Réitigh 9000=3200(10775^x

$$9000=3200( { 10775 }^{ x }$$

Réitigh do x.

$$x=\log_{10775}\left(\frac{45}{16}\right)\approx 0.11137055$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 3200.

$$\frac{9000}{3200}=10775^{x}$$

Laghdaigh an codán \frac{9000}{3200} chuig na téarmaí is ísle trí 200 a bhaint agus a chealú.

$$\frac{45}{16}=10775^{x}$$

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

$$10775^{x}=\frac{45}{16}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(10775^{x})=\log(\frac{45}{16})$$

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

$$x\log(10775)=\log(\frac{45}{16})$$

Roinn an dá thaobh faoi \log(10775).

$$x=\frac{\log(\frac{45}{16})}{\log(10775)}$$

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

$$x=\log_{10775}\left(\frac{45}{16}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10775)}+\log_{10775}\left(\frac{45}{16}\right)$$

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