Datrys 12^y-6=3

$$12 ^ { y - 6 } = 3$$

Datrys ar gyfer y

$$y=\log_{12}\left(8957952\right)\approx 6.442114109$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$12^{y-6}=3$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(12^{y-6})=\log(3)$$

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

$$\left(y-6\right)\log(12)=\log(3)$$

Rhannu’r ddwy ochr â \log(12).

$$y-6=\frac{\log(3)}{\log(12)}$$

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

$$y-6=\log_{12}\left(3\right)$$

Adio 6 at ddwy ochr yr hafaliad.

$$y=\log_{12}\left(3\right)-\left(-6\right)$$

Datrys ar gyfer y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(12)}+\log_{12}\left(8957952\right)$$

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