Datrys e^2x-9=0

$${ e }^{ 2x } -9=0$$

Datrys ar gyfer x

$$x=\ln(3)\approx 1.098612289$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{2x}-9=0$$

Adio 9 at ddwy ochr yr hafaliad.

$$e^{2x}=9$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{2x})=\log(9)$$

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

$$2x\log(e)=\log(9)$$

Rhannu’r ddwy ochr â \log(e).

$$2x=\frac{\log(9)}{\log(e)}$$

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

$$2x=\log_{e}\left(9\right)$$

Rhannu’r ddwy ochr â 2.

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

Datrys ar gyfer x (complex solution)

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

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