Datrys 2^2x+1=128

$${ 2 }^{ 2x+1 } = 128$$

Datrys ar gyfer x

$$x=3$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$2^{2x+1}=128$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{2x+1})=\log(128)$$

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

$$\left(2x+1\right)\log(2)=\log(128)$$

Rhannu’r ddwy ochr â \log(2).

$$2x+1=\frac{\log(128)}{\log(2)}$$

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

$$2x+1=\log_{2}\left(128\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$2x=7-1$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{6}{2}$$

Datrys ar gyfer x (complex solution)

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

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