Réitigh 23=40e^-0.2h

$$23 = 40 e ^ { - 0.2 h }$$

Réitigh do h.

$$h=\ln(\frac{102400000}{6436343})\approx 2.766926191$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 40.

$$\frac{23}{40}=e^{-0.2h}$$

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

$$e^{-0.2h}=\frac{23}{40}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{-0.2h})=\log(\frac{23}{40})$$

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

$$-0.2h\log(e)=\log(\frac{23}{40})$$

Roinn an dá thaobh faoi \log(e).

$$-0.2h=\frac{\log(\frac{23}{40})}{\log(e)}$$

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

$$-0.2h=\log_{e}\left(\frac{23}{40}\right)$$

Iolraigh an dá thaobh faoi -5.

$$h=\frac{\ln(\frac{23}{40})}{-0.2}$$