Datrys 2(3^x-1)=4

$$2 ( 3 ^ { x - 1 } ) = 4$$

Datrys ar gyfer x

$$x=\log_{3}\left(2\right)+1\approx 1.630929754$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$2\times 3^{x-1}=4$$

Rhannu’r ddwy ochr â 2.

$$3^{x-1}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{x-1})=\log(2)$$

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

$$\left(x-1\right)\log(3)=\log(2)$$

Rhannu’r ddwy ochr â \log(3).

$$x-1=\frac{\log(2)}{\log(3)}$$

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

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

Adio 1 at ddwy ochr yr hafaliad.

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

Datrys ar gyfer x (complex solution)

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

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