Datrys e^3x=8

$$e ^ { 3 x } = 8$$

Datrys ar gyfer x

$$x=\ln(2)\approx 0.693147181$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{3x}=8$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{3x})=\log(8)$$

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

$$3x\log(e)=\log(8)$$

Rhannu’r ddwy ochr â \log(e).

$$3x=\frac{\log(8)}{\log(e)}$$

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

$$3x=\log_{e}\left(8\right)$$

Rhannu’r ddwy ochr â 3.

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

Datrys ar gyfer x (complex solution)

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

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