Datrys e^-3x+1=4

$${ e }^{ -3x+1 } =4$$

Datrys ar gyfer x

$$x=\frac{1-2\ln(2)}{3}\approx -0.128764787$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$e^{-3x+1}=4$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-3x+1})=\log(4)$$

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

$$\left(-3x+1\right)\log(e)=\log(4)$$

Rhannu’r ddwy ochr â \log(e).

$$-3x+1=\frac{\log(4)}{\log(e)}$$

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

$$-3x+1=\log_{e}\left(4\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$-3x=2\ln(2)-1$$

Rhannu’r ddwy ochr â -3.

$$x=\frac{2\ln(2)-1}{-3}$$

Datrys ar gyfer x (complex solution)

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

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