Datrys 4^2x=100

$$4 ^ { 2 x } = 100$$

Datrys ar gyfer x

$$x = \frac{\log_{2} {(10)}}{2} \approx 1.660964047$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$4^{2x}=100$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{2x})=\log(100)$$

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

$$2x\log(4)=\log(100)$$

Rhannu’r ddwy ochr â \log(4).

$$2x=\frac{\log(100)}{\log(4)}$$

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

$$2x=\log_{4}\left(100\right)$$

Rhannu’r ddwy ochr â 2.

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