Datrys 52=4^x-12

$$52= { 4 }^{ x } -12$$

Datrys ar gyfer x

$$x=3$$

Camau gan Ddefnyddio Diffiniad Logarithm

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$4^{x}-12=52$$

Adio 12 at ddwy ochr yr hafaliad.

$$4^{x}=64$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{x})=\log(64)$$

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

$$x\log(4)=\log(64)$$

Rhannu’r ddwy ochr â \log(4).

$$x=\frac{\log(64)}{\log(4)}$$

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

$$x=\log_{4}\left(64\right)$$

Datrys ar gyfer x (complex solution)

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

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