Datrys 3^x=1/6

$$3 ^ { x } = \frac { 1 } { 6 }$$

Datrys ar gyfer x

$$x=-\log_{3}\left(6\right)\approx -1.630929754$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{x}=\frac{1}{6}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{x})=\log(\frac{1}{6})$$

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

$$x\log(3)=\log(\frac{1}{6})$$

Rhannu’r ddwy ochr â \log(3).

$$x=\frac{\log(\frac{1}{6})}{\log(3)}$$

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

$$x=\log_{3}\left(\frac{1}{6}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}-\log_{3}\left(6\right)$$

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