Réitigh 2^2x-(-6)=96

$$2 ^ { 2 x } - ( - 6 ) = 96$$

Réitigh do x.

$$x = \frac{\log_{2} {(90)}}{2} \approx 3.245926548$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Úsáid rialacha na n-easpónant agus na logartam chun an chothromóid a réiteach.

$$2^{2x}+6=96$$

Bain 6 ón dá thaobh den chothromóid.

$$2^{2x}=90$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{2x})=\log(90)$$

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

$$2x\log(2)=\log(90)$$

Roinn an dá thaobh faoi \log(2).

$$2x=\frac{\log(90)}{\log(2)}$$

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

$$2x=\log_{2}\left(90\right)$$

Roinn an dá thaobh faoi 2.

$$x=\frac{\log_{2}\left(90\right)}{2}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(90\right)}{2}$$

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