Datrys 3^x-2=81

$$3 ^ { x - 2 } = 81$$

Datrys ar gyfer x

$$x=6$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{x-2}=81$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{x-2})=\log(81)$$

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

$$\left(x-2\right)\log(3)=\log(81)$$

Rhannu’r ddwy ochr â \log(3).

$$x-2=\frac{\log(81)}{\log(3)}$$

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

$$x-2=\log_{3}\left(81\right)$$

Adio 2 at ddwy ochr yr hafaliad.

$$x=4-\left(-2\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+6$$

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