Datrys e^-0.0174z=0.5

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

Datrys ar gyfer z

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

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

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

Cymryd logarithm dwy ochr yr hafaliad.

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

Logarithm rhif wedi’i godi i bŵer yw’r pŵer wedi’i lluosi â logarithm y rhif.

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

Rhannu’r ddwy ochr â \log(e).

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

Gyda’r fformiwla newid-sail \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

Rhannu dwy ochr hafaliad â -0.0174, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

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