Datrys 5^2x+1div125=25,f

$$5 ^ { 2 x + 1 } \div 125 = 25 , f$$

Datrys ar gyfer x

$$x=2$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$\frac{1}{125}\times 5^{2x+1}=25$$

Lluosi’r ddwy ochr â 125.

$$5^{2x+1}=3125$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{2x+1})=\log(3125)$$

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

$$\left(2x+1\right)\log(5)=\log(3125)$$

Rhannu’r ddwy ochr â \log(5).

$$2x+1=\frac{\log(3125)}{\log(5)}$$

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

$$2x+1=\log_{5}\left(3125\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$2x=5-1$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{4}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(5)}+2$$

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