Datrys (16)^2x=589824

$$( 16 ) ^ { 2 x } = 589824$$

Datrys ar gyfer x

$$x = \frac{\log_{2} {(3)} + 8}{4} \approx 2.396240625$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$16^{2x}=589824$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(16^{2x})=\log(589824)$$

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

$$2x\log(16)=\log(589824)$$

Rhannu’r ddwy ochr â \log(16).

$$2x=\frac{\log(589824)}{\log(16)}$$

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

$$2x=\log_{16}\left(589824\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\log_{2}\left(768\right)}{2\times 2}$$

Datrys ar gyfer x (complex solution)

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

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