Réitigh 138*2^2x=46

$$138 \cdot 2 ^ { 2 x } = 46$$

Réitigh do x.

$$x=-\frac{\log_{2}\left(3\right)}{2}\approx -0.79248125$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$138\times 2^{2x}=46$$

Roinn an dá thaobh faoi 138.

$$2^{2x}=\frac{1}{3}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(2^{2x})=\log(\frac{1}{3})$$

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

$$2x\log(2)=\log(\frac{1}{3})$$

Roinn an dá thaobh faoi \log(2).

$$2x=\frac{\log(\frac{1}{3})}{\log(2)}$$

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

$$2x=\log_{2}\left(\frac{1}{3}\right)$$

Roinn an dá thaobh faoi 2.

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

Réitigh do x. (complex solution)

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

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