Datrys 9(4^3x-2)-7=3

$$9 ( 4 ^ { 3 x - 2 } ) - 7 = 3$$

Datrys ar gyfer x

$$x=\frac{\log_{2}\left(\frac{5}{9}\right)+5}{6}\approx 0.692000516$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$9\times 4^{3x-2}-7=3$$

Adio 7 at ddwy ochr yr hafaliad.

$$9\times 4^{3x-2}=10$$

Rhannu’r ddwy ochr â 9.

$$4^{3x-2}=\frac{10}{9}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{3x-2})=\log(\frac{10}{9})$$

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

$$\left(3x-2\right)\log(4)=\log(\frac{10}{9})$$

Rhannu’r ddwy ochr â \log(4).

$$3x-2=\frac{\log(\frac{10}{9})}{\log(4)}$$

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

$$3x-2=\log_{4}\left(\frac{10}{9}\right)$$

Adio 2 at ddwy ochr yr hafaliad.

$$3x=\frac{\ln(\frac{10}{9})}{2\ln(2)}-\left(-2\right)$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{\frac{\ln(\frac{10}{9})}{2\ln(2)}+2}{3}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{3\ln(2)}+\frac{\log_{2}\left(\frac{5}{9}\right)}{6}+\frac{5}{6}$$

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