Datrys 3^5x-2=4

$$3 ^ { 5 x - 2 } = 4$$

Datrys ar gyfer x

$$x=\frac{2\left(\log_{3}\left(2\right)+1\right)}{5}\approx 0.652371901$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{5x-2}=4$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{5x-2})=\log(4)$$

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

$$\left(5x-2\right)\log(3)=\log(4)$$

Rhannu’r ddwy ochr â \log(3).

$$5x-2=\frac{\log(4)}{\log(3)}$$

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

$$5x-2=\log_{3}\left(4\right)$$

Adio 2 at ddwy ochr yr hafaliad.

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

Rhannu’r ddwy ochr â 5.

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

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{5\ln(3)}+\frac{2\log_{3}\left(6\right)}{5}$$

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