Réitigh 2*(2/3)^x=5

$$2 \cdot ( \frac { 2 } { 3 } ) ^ { x } = 5$$

Réitigh do x.

$$x=\log_{\frac{2}{3}}\left(\frac{5}{2}\right)\approx -2.259851005$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$2\times \left(\frac{2}{3}\right)^{x}=5$$

Roinn an dá thaobh faoi 2.

$$\left(\frac{2}{3}\right)^{x}=\frac{5}{2}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(\left(\frac{2}{3}\right)^{x})=\log(\frac{5}{2})$$

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

$$x\log(\frac{2}{3})=\log(\frac{5}{2})$$

Roinn an dá thaobh faoi \log(\frac{2}{3}).

$$x=\frac{\log(\frac{5}{2})}{\log(\frac{2}{3})}$$

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

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

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{2}{3})}+\log_{\frac{2}{3}}\left(\frac{5}{2}\right)$$

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