Datrys (100)(102^2x)=500000

$$(100)( { 102 }^{ 2x } )=500000$$

Datrys ar gyfer x

$$x=\frac{\log_{102}\left(5000\right)}{2}\approx 0.920783055$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$100\times 102^{2x}=500000$$

Rhannu’r ddwy ochr â 100.

$$102^{2x}=5000$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(102^{2x})=\log(5000)$$

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

$$2x\log(102)=\log(5000)$$

Rhannu’r ddwy ochr â \log(102).

$$2x=\frac{\log(5000)}{\log(102)}$$

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

$$2x=\log_{102}\left(5000\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\log_{102}\left(5000\right)}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(102)}+\frac{\log_{102}\left(5000\right)}{2}$$

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