Datrys 5^x=1/125

$$5 ^ { x } = \frac { 1 } { 125 }$$

Datrys ar gyfer x

$$x=-3$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{x}=\frac{1}{125}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{x})=\log(\frac{1}{125})$$

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

$$x\log(5)=\log(\frac{1}{125})$$

Rhannu’r ddwy ochr â \log(5).

$$x=\frac{\log(\frac{1}{125})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{1}{125}\right)$$

Datrys ar gyfer x (complex solution)

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

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