Datrys e^2t=3

$$e ^ { 2 t } = 3$$

Datrys ar gyfer t

$$t=\frac{\ln(3)}{2}\approx 0.549306144$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{2t}=3$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{2t})=\log(3)$$

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

$$2t\log(e)=\log(3)$$

Rhannu’r ddwy ochr â \log(e).

$$2t=\frac{\log(3)}{\log(e)}$$

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

$$2t=\log_{e}\left(3\right)$$

Rhannu’r ddwy ochr â 2.

$$t=\frac{\ln(3)}{2}$$

Datrys ar gyfer t (complex solution)

$$t=\frac{\ln(3)}{2}+i\pi n_{1}$$

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