Réitigh 3^x+1=(273/10)^4

$$3 ^ { x + 1 } = ( \frac { 273 } { 10 } ) ^ { 4 }$$

Réitigh do x.

$$x=\log_{3}\left(\frac{68574961}{10000}\right)+3\approx 11.040231977$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$3^{x+1}=\frac{5554571841}{10000}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(3^{x+1})=\log(\frac{5554571841}{10000})$$

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

$$\left(x+1\right)\log(3)=\log(\frac{5554571841}{10000})$$

Roinn an dá thaobh faoi \log(3).

$$x+1=\frac{\log(\frac{5554571841}{10000})}{\log(3)}$$

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

$$x+1=\log_{3}\left(\frac{5554571841}{10000}\right)$$

Bain 1 ón dá thaobh den chothromóid.

$$x=\frac{\ln(\frac{5554571841}{10000})}{\ln(3)}-1$$

Réitigh do x. (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(\frac{68574961}{10000}\right)+3$$

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