Datrys 3e^2x=10

$$3 e ^ { 2 x } = 10$$

Datrys ar gyfer x

$$x=\frac{\ln(\frac{10}{3})}{2}\approx 0.601986402$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3e^{2x}=10$$

Rhannu’r ddwy ochr â 3.

$$e^{2x}=\frac{10}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{2x})=\log(\frac{10}{3})$$

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

$$2x\log(e)=\log(\frac{10}{3})$$

Rhannu’r ddwy ochr â \log(e).

$$2x=\frac{\log(\frac{10}{3})}{\log(e)}$$

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

$$2x=\log_{e}\left(\frac{10}{3}\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\ln(\frac{10}{3})}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\ln(\frac{10}{3})}{2}+\pi n_{1}i$$

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