Datrys 16^x=1/64

$$16 ^ { x } = \frac { 1 } { 64 }$$

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.

$$16^{x}=\frac{1}{64}$$

Cymryd logarithm dwy ochr yr hafaliad.

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

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

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

Rhannu’r ddwy ochr â \log(16).

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

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

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

Datrys ar gyfer x (complex solution)

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

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