Réitigh 700=135{(e)^-0.00866x}

$$700=135 {(e)^{ -0.00866x }}$$

Réitigh do x.

$$x=\frac{150000\ln(3)-50000\ln(140)}{433}\approx -190.046831017$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 135.

$$\frac{700}{135}=e^{-0.00866x}$$

Laghdaigh an codán \frac{700}{135} chuig na téarmaí is ísle trí 5 a bhaint agus a chealú.

$$\frac{140}{27}=e^{-0.00866x}$$

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

$$e^{-0.00866x}=\frac{140}{27}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{-0.00866x})=\log(\frac{140}{27})$$

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

$$-0.00866x\log(e)=\log(\frac{140}{27})$$

Roinn an dá thaobh faoi \log(e).

$$-0.00866x=\frac{\log(\frac{140}{27})}{\log(e)}$$

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

$$-0.00866x=\log_{e}\left(\frac{140}{27}\right)$$

Roinn an dá thaobh den chothromóid faoi -0.00866, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$x=\frac{\ln(\frac{140}{27})}{-0.00866}$$

Réitigh do x. (complex solution)

$$x=-\frac{i\times 100000\pi n_{1}}{433}+\frac{150000\ln(3)}{433}-\frac{50000\ln(140)}{433}$$

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