Datrys e^3x=30

$$e ^ { 3 x } = 30$$

Datrys ar gyfer x

$$x=\frac{\ln(30)}{3}\approx 1.133732461$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{3x}=30$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{3x})=\log(30)$$

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

$$3x\log(e)=\log(30)$$

Rhannu’r ddwy ochr â \log(e).

$$3x=\frac{\log(30)}{\log(e)}$$

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

$$3x=\log_{e}\left(30\right)$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{\ln(30)}{3}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3}+\frac{\ln(30)}{3}$$

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