Datrys 9^x=243

$$9 ^ { x } = 243$$

Datrys ar gyfer x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$9^{x}=243$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(9^{x})=\log(243)$$

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

$$x\log(9)=\log(243)$$

Rhannu’r ddwy ochr â \log(9).

$$x=\frac{\log(243)}{\log(9)}$$

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

$$x=\log_{9}\left(243\right)$$

Datrys ar gyfer x (complex solution)

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

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