Datrys (1/125)^x=25

$$( \frac { 1 } { 125 } ) ^ { x } = 25$$

Datrys ar gyfer x

$$x=-\frac{2}{3}\approx -0.666666667$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\left(\frac{1}{125}\right)^{x}=25$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{1}{125}\right)^{x})=\log(25)$$

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

$$x\log(\frac{1}{125})=\log(25)$$

Rhannu’r ddwy ochr â \log(\frac{1}{125}).

$$x=\frac{\log(25)}{\log(\frac{1}{125})}$$

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

$$x=\log_{\frac{1}{125}}\left(25\right)$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{2\pi n_{1}i}{3\ln(5)}-\frac{2}{3}$$

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