Datrys 8^4x=3

$$8 ^ { 4 x } = 3$$

Datrys ar gyfer x

$$x=\frac{\log_{2}\left(3\right)}{12}\approx 0.132080208$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$8^{4x}=3$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(8^{4x})=\log(3)$$

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

$$4x\log(8)=\log(3)$$

Rhannu’r ddwy ochr â \log(8).

$$4x=\frac{\log(3)}{\log(8)}$$

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

$$4x=\log_{8}\left(3\right)$$

Rhannu’r ddwy ochr â 4.

$$x=\frac{\log_{2}\left(3\right)}{3\times 4}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{6\ln(2)}+\frac{\log_{2}\left(3\right)}{12}$$

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