Datrys 4^2x-7=1/64

$$4 ^ { 2 x - 7 } = \frac { 1 } { 64 }$$

Datrys ar gyfer x

$$x=2$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$4^{2x-7}=\frac{1}{64}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(4^{2x-7})=\log(\frac{1}{64})$$

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

$$\left(2x-7\right)\log(4)=\log(\frac{1}{64})$$

Rhannu’r ddwy ochr â \log(4).

$$2x-7=\frac{\log(\frac{1}{64})}{\log(4)}$$

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

$$2x-7=\log_{4}\left(\frac{1}{64}\right)$$

Adio 7 at ddwy ochr yr hafaliad.

$$2x=-3-\left(-7\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{4}{2}$$

Datrys ar gyfer x (complex solution)

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

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