Réitigh 2097=5954.3{(e)^x*(-0.00896)}

$$2097=5954.3 {(e)^{ x \times (-0.00896) }}$$

Réitigh do x.

$$x=\frac{3125\ln(59543)-3125\ln(20970)}{28}\approx 116.473872288$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

Roinn an dá thaobh faoi 5954.3.

$$\frac{2097}{5954.3}=e^{x\left(-0.00896\right)}$$

Fairsingigh \frac{2097}{5954.3} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10.

$$\frac{20970}{59543}=e^{x\left(-0.00896\right)}$$

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

$$e^{x\left(-0.00896\right)}=\frac{20970}{59543}$$

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

$$e^{-0.00896x}=\frac{20970}{59543}$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{-0.00896x})=\log(\frac{20970}{59543})$$

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

$$-0.00896x\log(e)=\log(\frac{20970}{59543})$$

Roinn an dá thaobh faoi \log(e).

$$-0.00896x=\frac{\log(\frac{20970}{59543})}{\log(e)}$$

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

$$-0.00896x=\log_{e}\left(\frac{20970}{59543}\right)$$

Roinn an dá thaobh den chothromóid faoi -0.00896, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$x=\frac{\ln(\frac{20970}{59543})}{-0.00896}$$

Réitigh do x. (complex solution)

$$x=-\frac{i\times 3125\pi n_{1}}{14}+\frac{3125\ln(59543)}{28}-\frac{3125\ln(20970)}{28}$$

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