Datrys (5825)^(x-3)=120

$$( 5825 ) ^ { ( x - 3 ) } = 120$$

Datrys ar gyfer x

$$x=\log_{5825}\left(23717506875000\right)\approx 3.552195972$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5825^{x-3}=120$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5825^{x-3})=\log(120)$$

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

$$\left(x-3\right)\log(5825)=\log(120)$$

Rhannu’r ddwy ochr â \log(5825).

$$x-3=\frac{\log(120)}{\log(5825)}$$

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

$$x-3=\log_{5825}\left(120\right)$$

Adio 3 at ddwy ochr yr hafaliad.

$$x=\log_{5825}\left(120\right)-\left(-3\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5825)}+\log_{5825}\left(23717506875000\right)$$

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