Réitigh 6200=990(1115)^x+2900

$$6200 = 990 ( 1115 ) ^ { x } + 2900$$

Réitigh do x.

$$x=\log_{1115}\left(\frac{10}{3}\right)\approx 0.171588967$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$990\times 1115^{x}+2900=6200$$

Bain 2900 ón dá thaobh den chothromóid.

$$990\times 1115^{x}=3300$$

Roinn an dá thaobh faoi 990.

$$1115^{x}=\frac{10}{3}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(1115^{x})=\log(\frac{10}{3})$$

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

$$x\log(1115)=\log(\frac{10}{3})$$

Roinn an dá thaobh faoi \log(1115).

$$x=\frac{\log(\frac{10}{3})}{\log(1115)}$$

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

$$x=\log_{1115}\left(\frac{10}{3}\right)$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(1115)}+\log_{1115}\left(\frac{10}{3}\right)$$

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