Datrys 64^n=16

$$64 ^ { n } = 16$$

Datrys ar gyfer n

$$n=\frac{2}{3}\approx 0.666666667$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$64^{n}=16$$

Cymryd logarithm dwy ochr yr hafaliad.

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

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

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

Rhannu’r ddwy ochr â \log(64).

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

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

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

Datrys ar gyfer n (complex solution)

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

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