Réitigh 3^x+118/3=19

$${ 3 }^{ x+1 } \frac{ 18 }{ 3 } =19$$

Réitigh do x.

$$x=-\log_{3}\left(\frac{2}{19}\right)-2\approx 0.049214106$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$6\times 3^{x+1}=19$$

Roinn an dá thaobh faoi 6.

$$3^{x+1}=\frac{19}{6}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(3^{x+1})=\log(\frac{19}{6})$$

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

$$\left(x+1\right)\log(3)=\log(\frac{19}{6})$$

Roinn an dá thaobh faoi \log(3).

$$x+1=\frac{\log(\frac{19}{6})}{\log(3)}$$

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

$$x+1=\log_{3}\left(\frac{19}{6}\right)$$

Bain 1 ón dá thaobh den chothromóid.

$$x=\frac{\ln(\frac{19}{6})}{\ln(3)}-1$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}-\log_{3}\left(\frac{2}{19}\right)-2$$

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