Datrys 8^p=60

$$8 ^ { p } = 60$$

Datrys ar gyfer p

$$p = \frac{\log_{2} {(60)}}{3} \approx 1.968963532$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$8^{p}=60$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(8^{p})=\log(60)$$

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

$$p\log(8)=\log(60)$$

Rhannu’r ddwy ochr â \log(8).

$$p=\frac{\log(60)}{\log(8)}$$

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

$$p=\log_{8}\left(60\right)$$

Datrys ar gyfer p (complex solution)

$$p=\frac{2\pi n_{1}i}{3\ln(2)}+\frac{\log_{2}\left(60\right)}{3}$$

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