Réitigh e^-0.0174z=0.5

$${ e }^{ -0.0174z } =0.5$$

Réitigh do z.

$$z=\frac{5000\ln(2)}{87}\approx 39.83604486$$

Céimeanna ag Baint Úsáid as Sainiú an Logartaim

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

$$e^{-0.0174z}=0.5$$

Ghlac logartam an dá thaobh den chothromóid.

$$\log(e^{-0.0174z})=\log(0.5)$$

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

$$-0.0174z\log(e)=\log(0.5)$$

Roinn an dá thaobh faoi \log(e).

$$-0.0174z=\frac{\log(0.5)}{\log(e)}$$

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

$$-0.0174z=\log_{e}\left(0.5\right)$$

Roinn an dá thaobh den chothromóid faoi -0.0174, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$z=-\frac{\ln(2)}{-0.0174}$$

Réitigh do z. (complex solution)

$$z=-\frac{i\times 10000\pi n_{1}}{87}+\frac{5000\ln(2)}{87}$$

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