Datrys 9^x-4=81

$$9 ^ { x - 4 } = 81$$

Datrys ar gyfer x

$$x=6$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$9^{x-4}=81$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(9^{x-4})=\log(81)$$

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

$$\left(x-4\right)\log(9)=\log(81)$$

Rhannu’r ddwy ochr â \log(9).

$$x-4=\frac{\log(81)}{\log(9)}$$

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

$$x-4=\log_{9}\left(81\right)$$

Adio 4 at ddwy ochr yr hafaliad.

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

Datrys ar gyfer x (complex solution)

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

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