Datrys 4^x=100

$$4 ^ { x } = 100$$

Datrys ar gyfer x

$$x=\log_{2}\left(10\right)\approx 3.321928095$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$4^{x}=100$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{x})=\log(100)$$

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

$$x\log(4)=\log(100)$$

Rhannu’r ddwy ochr â \log(4).

$$x=\frac{\log(100)}{\log(4)}$$

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

$$x=\log_{4}\left(100\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}+\log_{2}\left(10\right)$$

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