Datrys 33^x=243

$$33 ^ { x } = 243$$

Datrys ar gyfer x

$$x=5\log_{33}\left(3\right)\approx 1.571013746$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$33^{x}=243$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(33^{x})=\log(243)$$

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

$$x\log(33)=\log(243)$$

Rhannu’r ddwy ochr â \log(33).

$$x=\frac{\log(243)}{\log(33)}$$

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

$$x=\log_{33}\left(243\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(33)}+5\log_{33}\left(3\right)$$

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