Datrys 138*2^2x=46

$$138 \cdot 2 ^ { 2 x } = 46$$

Datrys ar gyfer x

$$x=-\frac{\log_{2}\left(3\right)}{2}\approx -0.79248125$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$138\times 2^{2x}=46$$

Rhannu’r ddwy ochr â 138.

$$2^{2x}=\frac{1}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{2x})=\log(\frac{1}{3})$$

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

$$2x\log(2)=\log(\frac{1}{3})$$

Rhannu’r ddwy ochr â \log(2).

$$2x=\frac{\log(\frac{1}{3})}{\log(2)}$$

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

$$2x=\log_{2}\left(\frac{1}{3}\right)$$

Rhannu’r ddwy ochr â 2.

$$x=-\frac{\log_{2}\left(3\right)}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(2)}-\frac{\log_{2}\left(3\right)}{2}$$

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