Datrys (500)^x+1=(500)^-5

$$( 500 ) ^ { x + 1 } = ( 500 ) ^ { - 5 }$$

Datrys ar gyfer x

$$x=-6$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$500^{x+1}=\frac{1}{31250000000000}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(500^{x+1})=\log(\frac{1}{31250000000000})$$

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

$$\left(x+1\right)\log(500)=\log(\frac{1}{31250000000000})$$

Rhannu’r ddwy ochr â \log(500).

$$x+1=\frac{\log(\frac{1}{31250000000000})}{\log(500)}$$

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

$$x+1=\log_{500}\left(\frac{1}{31250000000000}\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$x=-5-1$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(500)}-6$$

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