Datrys 0.25={(e)^-2x}

$$0.25= {(e)^{ -2x }}$$

Datrys ar gyfer x

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

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$e^{-2x}=0.25$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-2x})=\log(0.25)$$

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

$$-2x\log(e)=\log(0.25)$$

Rhannu’r ddwy ochr â \log(e).

$$-2x=\frac{\log(0.25)}{\log(e)}$$

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

$$-2x=\log_{e}\left(0.25\right)$$

Rhannu’r ddwy ochr â -2.

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

Datrys ar gyfer x (complex solution)

$$x=-i\pi n_{1}+\ln(2)$$

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