Datrys 5^2x=15

$${ 5 }^{ 2x } =15$$

Datrys ar gyfer x

$$x=\frac{\log_{5}\left(15\right)}{2}\approx 0.841303097$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{2x}=15$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{2x})=\log(15)$$

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

$$2x\log(5)=\log(15)$$

Rhannu’r ddwy ochr â \log(5).

$$2x=\frac{\log(15)}{\log(5)}$$

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

$$2x=\log_{5}\left(15\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\log_{5}\left(15\right)}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(5)}+\frac{\log_{5}\left(15\right)}{2}$$

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