Datrys 8^x=128

$${ 8 }^{ x } =128$$

Datrys ar gyfer x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$8^{x}=128$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(8^{x})=\log(128)$$

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

$$x\log(8)=\log(128)$$

Rhannu’r ddwy ochr â \log(8).

$$x=\frac{\log(128)}{\log(8)}$$

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

$$x=\log_{8}\left(128\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{7}{3}$$

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