Réitigh (16)^2x=589824

$$( 16 ) ^ { 2 x } = 589824$$

Réitigh do x.

$$x = \frac{\log_{2} {(3)} + 8}{4} \approx 2.396240625$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$16^{2x}=589824$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(16^{2x})=\log(589824)$$

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

$$2x\log(16)=\log(589824)$$

Roinn an dá thaobh faoi \log(16).

$$2x=\frac{\log(589824)}{\log(16)}$$

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

$$2x=\log_{16}\left(589824\right)$$

Roinn an dá thaobh faoi 2.

$$x=\frac{\log_{2}\left(768\right)}{2\times 2}$$

Réitigh do x. (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(2)}+\frac{\log_{2}\left(3\right)}{4}+2$$

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