Datrys (1/16)^2x=64

$$( \frac { 1 } { 16 } ) ^ { 2 x } = 64$$

Datrys ar gyfer x

$$x=-\frac{3}{4}=-0.75$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\left(\frac{1}{16}\right)^{2x}=64$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{1}{16}\right)^{2x})=\log(64)$$

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

$$2x\log(\frac{1}{16})=\log(64)$$

Rhannu’r ddwy ochr â \log(\frac{1}{16}).

$$2x=\frac{\log(64)}{\log(\frac{1}{16})}$$

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

$$2x=\log_{\frac{1}{16}}\left(64\right)$$

Rhannu’r ddwy ochr â 2.

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

Datrys ar gyfer x (complex solution)

$$x=-\frac{i\pi n_{1}}{4\ln(2)}-\frac{3}{4}$$

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