Datrys (2/5)^x=125/8

$$( \frac { 2 } { 5 } ) ^ { x } = \frac { 125 } { 8 }$$

Datrys ar gyfer x

$$x=-3$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{2}{5}\right)^{x})=\log(\frac{125}{8})$$

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

$$x\log(\frac{2}{5})=\log(\frac{125}{8})$$

Rhannu’r ddwy ochr â \log(\frac{2}{5}).

$$x=\frac{\log(\frac{125}{8})}{\log(\frac{2}{5})}$$

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

$$x=\log_{\frac{2}{5}}\left(\frac{125}{8}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{2}{5})}+\log_{\frac{2}{5}}\left(\frac{125}{8}\right)$$

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