Réitigh 293=336e^r(39)

$$293 = 336 e ^ { r ( 39 ) }$$

Réitigh do r.

$$r=\frac{\ln(\frac{293}{336})}{39}\approx -0.003511245$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 336.

$$\frac{293}{336}=e^{r\times 39}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$e^{r\times 39}=\frac{293}{336}$$

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

$$e^{39r}=\frac{293}{336}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{39r})=\log(\frac{293}{336})$$

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

$$39r\log(e)=\log(\frac{293}{336})$$

Roinn an dá thaobh faoi \log(e).

$$39r=\frac{\log(\frac{293}{336})}{\log(e)}$$

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

$$39r=\log_{e}\left(\frac{293}{336}\right)$$

Roinn an dá thaobh faoi 39.

$$r=\frac{\ln(\frac{293}{336})}{39}$$

Réitigh do r. (complex solution)

$$r=\frac{2\pi n_{1}i}{39}+\frac{\ln(\frac{293}{336})}{39}$$

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