Datrys 3^2x-3=9

$$3 ^ { 2 x - 3 } = 9$$

Datrys ar gyfer x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3^{2x-3}=9$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(3^{2x-3})=\log(9)$$

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

$$\left(2x-3\right)\log(3)=\log(9)$$

Rhannu’r ddwy ochr â \log(3).

$$2x-3=\frac{\log(9)}{\log(3)}$$

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

$$2x-3=\log_{3}\left(9\right)$$

Adio 3 at ddwy ochr yr hafaliad.

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

Rhannu’r ddwy ochr â 2.

$$x=\frac{5}{2}$$

Datrys ar gyfer x (complex solution)

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

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