Datrys 2^-x=3/2

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

Datrys ar gyfer x

$$x=-\log_{2}\left(3\right)+1\approx -0.584962501$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

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

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{-x})=\log(\frac{3}{2})$$

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

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

Rhannu’r ddwy ochr â \log(2).

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

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

$$-x=\log_{2}\left(\frac{3}{2}\right)$$

Rhannu’r ddwy ochr â -1.

$$x=\frac{\log_{2}\left(3\right)-1}{-1}$$

Datrys ar gyfer x (complex solution)

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

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