Datrys e^-0.66t=0.37

$$e ^ { - 0.66 t } = 0.37$$

Datrys ar gyfer t

$$t=\frac{100\ln(10)-50\ln(37)}{33}\approx 1.506442838$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{-0.66t}=0.37$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-0.66t})=\log(0.37)$$

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

$$-0.66t\log(e)=\log(0.37)$$

Rhannu’r ddwy ochr â \log(e).

$$-0.66t=\frac{\log(0.37)}{\log(e)}$$

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

$$-0.66t=\log_{e}\left(0.37\right)$$

Rhannu dwy ochr hafaliad â -0.66, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

$$t=\frac{\ln(\frac{37}{100})}{-0.66}$$

Datrys ar gyfer t (complex solution)

$$t=-\frac{i\times 100\pi n_{1}}{33}+\frac{100\ln(10)}{33}-\frac{50\ln(37)}{33}$$

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