Datrys 2^-2x=8

$$2 ^ { - 2 x } = 8$$

Datrys ar gyfer x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$2^{-2x}=8$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{-2x})=\log(8)$$

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

$$-2x\log(2)=\log(8)$$

Rhannu’r ddwy ochr â \log(2).

$$-2x=\frac{\log(8)}{\log(2)}$$

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

$$-2x=\log_{2}\left(8\right)$$

Rhannu’r ddwy ochr â -2.

$$x=\frac{3}{-2}$$

Datrys ar gyfer x (complex solution)

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

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