Datrys (1/3)^x=211/560

$$( \frac { 1 } { 3 } ) ^ { x } = \frac { 211 } { 560 }$$

Datrys ar gyfer x

$$x=-\log_{3}\left(\frac{211}{560}\right)\approx 0.888465076$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\left(\frac{1}{3}\right)^{x}=\frac{211}{560}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{1}{3}\right)^{x})=\log(\frac{211}{560})$$

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

$$x\log(\frac{1}{3})=\log(\frac{211}{560})$$

Rhannu’r ddwy ochr â \log(\frac{1}{3}).

$$x=\frac{\log(\frac{211}{560})}{\log(\frac{1}{3})}$$

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

$$x=\log_{\frac{1}{3}}\left(\frac{211}{560}\right)$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{2\pi n_{1}i}{\ln(3)}-\log_{3}\left(\frac{211}{560}\right)$$

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