Réitigh 19=7+17e^-0.034t

$$19 = 7 + 17 e ^ { - 0.034 t }$$

Réitigh do t.

$$t=\frac{500\ln(17)-500\ln(12)}{17}\approx 10.244314537$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$7+17e^{-0.034t}=19$$

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

$$17e^{-0.034t}+7=19$$

Bain 7 ón dá thaobh den chothromóid.

$$17e^{-0.034t}=12$$

Roinn an dá thaobh faoi 17.

$$e^{-0.034t}=\frac{12}{17}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{-0.034t})=\log(\frac{12}{17})$$

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

$$-0.034t\log(e)=\log(\frac{12}{17})$$

Roinn an dá thaobh faoi \log(e).

$$-0.034t=\frac{\log(\frac{12}{17})}{\log(e)}$$

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

$$-0.034t=\log_{e}\left(\frac{12}{17}\right)$$

Roinn an dá thaobh den chothromóid faoi -0.034, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$t=\frac{\ln(\frac{12}{17})}{-0.034}$$

Réitigh do t. (complex solution)

$$t=-\frac{i\times 1000\pi n_{1}}{17}+\frac{500\ln(17)}{17}-\frac{500\ln(12)}{17}$$

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