Datrys 4^2x+3=1

$$4 ^ { 2 x + 3 } = 1$$

Datrys ar gyfer x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$4^{2x+3}=1$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{2x+3})=\log(1)$$

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

$$\left(2x+3\right)\log(4)=\log(1)$$

Rhannu’r ddwy ochr â \log(4).

$$2x+3=\frac{\log(1)}{\log(4)}$$

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

$$2x+3=\log_{4}\left(1\right)$$

Tynnu 3 o ddwy ochr yr hafaliad.

$$2x=-3$$

Rhannu’r ddwy ochr â 2.

$$x=-\frac{3}{2}$$

Datrys ar gyfer x (complex solution)

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

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