Datrys 23^2x+1=54

$$23 ^ { 2 x + 1 } = 54$$

Datrys ar gyfer x

$$x=\frac{\log_{23}\left(54\right)-1}{2}\approx 0.136101324$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$23^{2x+1}=54$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(23^{2x+1})=\log(54)$$

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

$$\left(2x+1\right)\log(23)=\log(54)$$

Rhannu’r ddwy ochr â \log(23).

$$2x+1=\frac{\log(54)}{\log(23)}$$

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

$$2x+1=\log_{23}\left(54\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$2x=\log_{23}\left(54\right)-1$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\log_{23}\left(54\right)-1}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(23)}+\frac{\log_{23}\left(54\right)}{2}-\frac{1}{2}$$

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