Datrys 16^x=64

$$16 ^ { x } = 64$$

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.

$$16^{x}=64$$

Cymryd logarithm dwy ochr yr hafaliad.

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

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

$$x\log(16)=\log(64)$$

Rhannu’r ddwy ochr â \log(16).

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

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

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

Datrys ar gyfer x (complex solution)

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

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