Réitigh 8000=6500e^.06x

$$8000=6500 { e }^{ .06x }$$

Réitigh do x.

$$x=\frac{200\ln(2)-50\ln(13)}{3}\approx 3.46065608$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 6500.

$$\frac{8000}{6500}=e^{0.06x}$$

Laghdaigh an codán \frac{8000}{6500} chuig na téarmaí is ísle trí 500 a bhaint agus a chealú.

$$\frac{16}{13}=e^{0.06x}$$

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

$$e^{0.06x}=\frac{16}{13}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{0.06x})=\log(\frac{16}{13})$$

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

$$0.06x\log(e)=\log(\frac{16}{13})$$

Roinn an dá thaobh faoi \log(e).

$$0.06x=\frac{\log(\frac{16}{13})}{\log(e)}$$

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

$$0.06x=\log_{e}\left(\frac{16}{13}\right)$$

Roinn an dá thaobh den chothromóid faoi 0.06, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$x=\frac{\ln(\frac{16}{13})}{0.06}$$

Réitigh do x. (complex solution)

$$x=\frac{i\times 100\pi n_{1}}{3}+\frac{200\ln(2)}{3}-\frac{50\ln(13)}{3}$$

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