Datrys e^2x-1=3

$$e ^ { 2 x - 1 } = 3$$

Datrys ar gyfer x

$$x = \frac{\log_{e} {(3)} + 1}{2} \approx 1.049306144$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{2x-1}=3$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{2x-1})=\log(3)$$

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

$$\left(2x-1\right)\log(e)=\log(3)$$

Rhannu’r ddwy ochr â \log(e).

$$2x-1=\frac{\log(3)}{\log(e)}$$

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

$$2x-1=\log_{e}\left(3\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$2x=\ln(3)-\left(-1\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\ln(3)+1}{2}$$

Datrys ar gyfer x (complex solution)

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

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