Datrys 5^x=256

$$5 ^ { x } = 256$$

Datrys ar gyfer x

$$x=8\log_{5}\left(2\right)\approx 3.445412465$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{x}=256$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{x})=\log(256)$$

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

$$x\log(5)=\log(256)$$

Rhannu’r ddwy ochr â \log(5).

$$x=\frac{\log(256)}{\log(5)}$$

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

$$x=\log_{5}\left(256\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+8\log_{5}\left(2\right)$$

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