Datrys 60e^-0.17t=10

$$60 e ^ { - 0.17 t } = 10$$

Datrys ar gyfer t

$$t=\frac{100\ln(6)}{17}\approx 10.539761584$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$60e^{-0.17t}=10$$

Rhannu’r ddwy ochr â 60.

$$e^{-0.17t}=\frac{1}{6}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-0.17t})=\log(\frac{1}{6})$$

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

$$-0.17t\log(e)=\log(\frac{1}{6})$$

Rhannu’r ddwy ochr â \log(e).

$$-0.17t=\frac{\log(\frac{1}{6})}{\log(e)}$$

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

$$-0.17t=\log_{e}\left(\frac{1}{6}\right)$$

Rhannu dwy ochr hafaliad â -0.17, sydd yr un peth â lluosi’r ddwy ochr â chilydd y ffracsiwn.

$$t=-\frac{\ln(6)}{-0.17}$$

Datrys ar gyfer t (complex solution)

$$t=-\frac{i\times 200\pi n_{1}}{17}+\frac{100\ln(6)}{17}$$

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