Datrys 23^2x=18

$$23 ^ { 2 x } = 18$$

Datrys ar gyfer x

$$x=\frac{\log_{23}\left(18\right)}{2}\approx 0.460911671$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$23^{2x}=18$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(23^{2x})=\log(18)$$

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

$$2x\log(23)=\log(18)$$

Rhannu’r ddwy ochr â \log(23).

$$2x=\frac{\log(18)}{\log(23)}$$

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

$$2x=\log_{23}\left(18\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\log_{23}\left(18\right)}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(23)}+\frac{\log_{23}\left(18\right)}{2}$$

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