Datrys e^4x=5

$$e ^ { 4 x } = 5$$

Datrys ar gyfer x

$$x=\frac{\ln(5)}{4}\approx 0.402359478$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{4x}=5$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{4x})=\log(5)$$

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

$$4x\log(e)=\log(5)$$

Rhannu’r ddwy ochr â \log(e).

$$4x=\frac{\log(5)}{\log(e)}$$

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

$$4x=\log_{e}\left(5\right)$$

Rhannu’r ddwy ochr â 4.

$$x=\frac{\ln(5)}{4}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{2}+\frac{\ln(5)}{4}$$

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