Datrys 6^-3x=4

$$6 ^ { - 3 x } = 4$$

Datrys ar gyfer x

$$x=-\frac{2\log_{6}\left(2\right)}{3}\approx -0.257901871$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$6^{-3x}=4$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(6^{-3x})=\log(4)$$

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

$$-3x\log(6)=\log(4)$$

Rhannu’r ddwy ochr â \log(6).

$$-3x=\frac{\log(4)}{\log(6)}$$

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

$$-3x=\log_{6}\left(4\right)$$

Rhannu’r ddwy ochr â -3.

$$x=\frac{2\log_{6}\left(2\right)}{-3}$$

Datrys ar gyfer x (complex solution)

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

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