Réitigh 73=2^2x+3

$$73 = 2 ^ { 2 x + 3 }$$

Réitigh do x.

$$x = \frac{\log_{2} {(73)} - 3}{2} \approx 1.594912279$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$2^{2x+3}=73$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{2x+3})=\log(73)$$

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

$$\left(2x+3\right)\log(2)=\log(73)$$

Roinn an dá thaobh faoi \log(2).

$$2x+3=\frac{\log(73)}{\log(2)}$$

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

$$2x+3=\log_{2}\left(73\right)$$

Bain 3 ón dá thaobh den chothromóid.

$$2x=\log_{2}\left(73\right)-3$$

Roinn an dá thaobh faoi 2.

$$x=\frac{\log_{2}\left(73\right)-3}{2}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(73\right)}{2}-\frac{3}{2}$$

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