Datrys 3^3x+1-1=7+5

$$3 ^ { 3 x + 1 } - 1 = 7 + 5$$

Datrys ar gyfer x

$$x=\frac{\log_{3}\left(13\right)-1}{3}\approx 0.44490584$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{3x+1}-1=12$$

Adio 1 at ddwy ochr yr hafaliad.

$$3^{3x+1}=13$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{3x+1})=\log(13)$$

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

$$\left(3x+1\right)\log(3)=\log(13)$$

Rhannu’r ddwy ochr â \log(3).

$$3x+1=\frac{\log(13)}{\log(3)}$$

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

$$3x+1=\log_{3}\left(13\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$3x=\log_{3}\left(13\right)-1$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{\log_{3}\left(13\right)-1}{3}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(3)}+\frac{\log_{3}\left(13\right)}{3}-\frac{1}{3}$$

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