Datrys e^x-1=2

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

Datrys ar gyfer x

$$x=\ln(2)+1\approx 1.693147181$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

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

Cymryd logarithm dwy ochr yr hafaliad.

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

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

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

Rhannu’r ddwy ochr â \log(e).

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

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

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

Adio 1 at ddwy ochr yr hafaliad.

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

Datrys ar gyfer x (complex solution)

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

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