Datrys 255=2^n-1

$$255 = 2 ^ { n } - 1$$

Datrys ar gyfer n

$$n=8$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$2^{n}-1=255$$

Adio 1 at ddwy ochr yr hafaliad.

$$2^{n}=256$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{n})=\log(256)$$

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

$$n\log(2)=\log(256)$$

Rhannu’r ddwy ochr â \log(2).

$$n=\frac{\log(256)}{\log(2)}$$

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

$$n=\log_{2}\left(256\right)$$