Datrys 3(6)^2x-3=648

$$3 ( 6 ) ^ { 2 x - 3 } = 648$$

Datrys ar gyfer x

$$x=3$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3\times 6^{2x-3}=648$$

Rhannu’r ddwy ochr â 3.

$$6^{2x-3}=216$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(6^{2x-3})=\log(216)$$

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

$$\left(2x-3\right)\log(6)=\log(216)$$

Rhannu’r ddwy ochr â \log(6).

$$2x-3=\frac{\log(216)}{\log(6)}$$

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

$$2x-3=\log_{6}\left(216\right)$$

Adio 3 at ddwy ochr yr hafaliad.

$$2x=3-\left(-3\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{6}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(6)}+3$$

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