Datrys 2^2x=104/7

$$2 ^ { 2 x } = \frac { 104 } { 7 }$$

Datrys ar gyfer x

$$x = \frac{\log_{2} {(\frac{13}{7})} + 3}{2} \approx 1.946542398$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$2^{2x}=\frac{104}{7}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{2x})=\log(\frac{104}{7})$$

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

$$2x\log(2)=\log(\frac{104}{7})$$

Rhannu’r ddwy ochr â \log(2).

$$2x=\frac{\log(\frac{104}{7})}{\log(2)}$$

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

$$2x=\log_{2}\left(\frac{104}{7}\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\ln(\frac{104}{7})}{2\ln(2)}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\frac{\log_{2}\left(\frac{13}{7}\right)}{2}+\frac{3}{2}$$

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