Datrys 2^x+1+1=100001_{2}

$$2 ^ { x + 1 } + 1 = 100001 _ { 2 }$$

Datrys ar gyfer x

$$x=5\log_{2}\left(5\right)+4\approx 15.609640474$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$2^{x+1}+1=100001$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$2^{x+1}=100000$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{x+1})=\log(100000)$$

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

$$\left(x+1\right)\log(2)=\log(100000)$$

Rhannu’r ddwy ochr â \log(2).

$$x+1=\frac{\log(100000)}{\log(2)}$$

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

$$x+1=\log_{2}\left(100000\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$x=5\log_{2}\left(10\right)-1$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+5\log_{2}\left(5\right)+4$$

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