Datrys 1/5e^6x=4

$$\frac { 1 } { 5 } e ^ { 6 x } = 4$$

Datrys ar gyfer x

$$x=\frac{\ln(20)}{6}\approx 0.499288712$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\frac{1}{5}e^{6x}=4$$

Lluosi’r ddwy ochr â 5.

$$e^{6x}=20$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{6x})=\log(20)$$

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

$$6x\log(e)=\log(20)$$

Rhannu’r ddwy ochr â \log(e).

$$6x=\frac{\log(20)}{\log(e)}$$

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

$$6x=\log_{e}\left(20\right)$$

Rhannu’r ddwy ochr â 6.

$$x=\frac{\ln(20)}{6}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{3}+\frac{\ln(20)}{6}$$

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