Datrys 5.2^2x+1=320

$$5.2 ^ { 2 x + 1 } = 320$$

Datrys ar gyfer x

$$x=-\frac{\log_{5.2}\left(0.01625\right)}{2}\approx 1.24939824$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5.2^{2x+1}=320$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5.2^{2x+1})=\log(320)$$

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

$$\left(2x+1\right)\log(5.2)=\log(320)$$

Rhannu’r ddwy ochr â \log(5.2).

$$2x+1=\frac{\log(320)}{\log(5.2)}$$

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

$$2x+1=\log_{5.2}\left(320\right)$$

Tynnu 1 o ddwy ochr yr hafaliad.

$$2x=\frac{\ln(320)}{\ln(\frac{26}{5})}-1$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\frac{\ln(320)}{\ln(\frac{26}{5})}-1}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(5.2)}-\frac{\log_{5.2}\left(0.01625\right)}{2}$$

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