Datrys 16^x+2/4=5

$$16 ^ { x } + 2 / 4 = 5$$

Datrys ar gyfer x

$$x=\frac{\log_{2}\left(3\right)}{2}-\frac{1}{4}\approx 0.54248125$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$16^{x}+\frac{1}{2}=5$$

Tynnu \frac{1}{2} o ddwy ochr yr hafaliad.

$$16^{x}=\frac{9}{2}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(16^{x})=\log(\frac{9}{2})$$

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

$$x\log(16)=\log(\frac{9}{2})$$

Rhannu’r ddwy ochr â \log(16).

$$x=\frac{\log(\frac{9}{2})}{\log(16)}$$

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

$$x=\log_{16}\left(\frac{9}{2}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{2\ln(2)}+\frac{\log_{2}\left(3\right)}{2}-\frac{1}{4}$$

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