Datrys 3^3x-1=32

$$3 ^ { 3 x - 1 } = 32$$

Datrys ar gyfer x

$$x = \frac{5 \log_{3} {(2)} + 1}{3} \approx 1.384882923$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{3x-1}=32$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{3x-1})=\log(32)$$

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

$$\left(3x-1\right)\log(3)=\log(32)$$

Rhannu’r ddwy ochr â \log(3).

$$3x-1=\frac{\log(32)}{\log(3)}$$

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

$$3x-1=\log_{3}\left(32\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$3x=5\log_{3}\left(2\right)-\left(-1\right)$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{5\log_{3}\left(2\right)+1}{3}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(3)}+\frac{5\log_{3}\left(2\right)}{3}+\frac{1}{3}$$

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