Réitigh 32^3x-2-48=0

$$32 ^ { 3 x - 2 } - 48 = 0$$

Réitigh do x.

$$x = \frac{\log_{2} {(3)} + 14}{15} \approx 1.0389975$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$32^{3x-2}-48=0$$

Cuir 48 leis an dá thaobh den chothromóid.

$$32^{3x-2}=48$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(32^{3x-2})=\log(48)$$

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

$$\left(3x-2\right)\log(32)=\log(48)$$

Roinn an dá thaobh faoi \log(32).

$$3x-2=\frac{\log(48)}{\log(32)}$$

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

$$3x-2=\log_{32}\left(48\right)$$

Cuir 2 leis an dá thaobh den chothromóid.

$$3x=\frac{\log_{2}\left(48\right)}{5}-\left(-2\right)$$

Roinn an dá thaobh faoi 3.

$$x=\frac{\frac{\log_{2}\left(48\right)}{5}+2}{3}$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{15\ln(2)}+\frac{\log_{2}\left(3\right)}{15}+\frac{14}{15}$$

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