Datrys 4^-x=37

$$4 ^ { - x } = 37$$

Datrys ar gyfer x

$$x = -\frac{\log_{2} {(37)}}{2} \approx -2.604726683$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$4^{-x}=37$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{-x})=\log(37)$$

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

$$-x\log(4)=\log(37)$$

Rhannu’r ddwy ochr â \log(4).

$$-x=\frac{\log(37)}{\log(4)}$$

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

$$-x=\log_{4}\left(37\right)$$

Rhannu’r ddwy ochr â -1.

$$x=\frac{\log_{2}\left(37\right)}{-2}$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(37\right)}{2}$$

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