Datrys (0.1)^2x=100

$$( 0.1 ) ^ { 2 x } = 100$$

Datrys ar gyfer x

$$x=-1$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$0.1^{2x}=100$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(0.1^{2x})=\log(100)$$

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

$$2x\log(0.1)=\log(100)$$

Rhannu’r ddwy ochr â \log(0.1).

$$2x=\frac{\log(100)}{\log(0.1)}$$

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

$$2x=\log_{0.1}\left(100\right)$$

Rhannu’r ddwy ochr â 2.

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

Datrys ar gyfer x (complex solution)

$$x=-i\pi n_{1}\log(e)-1$$

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