Datrys 3^3x+1-27=0

$$3 ^ { 3 x + 1 } - 27 = 0$$

Datrys ar gyfer x

$$x=\frac{2}{3}\approx 0.666666667$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{3x+1}-27=0$$

Adio 27 at ddwy ochr yr hafaliad.

$$3^{3x+1}=27$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{3x+1})=\log(27)$$

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

$$\left(3x+1\right)\log(3)=\log(27)$$

Rhannu’r ddwy ochr â \log(3).

$$3x+1=\frac{\log(27)}{\log(3)}$$

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

$$3x+1=\log_{3}\left(27\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$3x=3-1$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{2}{3}$$

Datrys ar gyfer x (complex solution)

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

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