Datrys 3(5^2x-1)+14=92

$$3 ( 5 ^ { 2 x - 1 } ) + 14 = 92$$

Datrys ar gyfer x

$$x = \frac{\log_{5} {(26)} + 1}{2} \approx 1.5121846$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3\times 5^{2x-1}+14=92$$

Tynnu 14 o ddwy ochr yr hafaliad.

$$3\times 5^{2x-1}=78$$

Rhannu’r ddwy ochr â 3.

$$5^{2x-1}=26$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{2x-1})=\log(26)$$

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

$$\left(2x-1\right)\log(5)=\log(26)$$

Rhannu’r ddwy ochr â \log(5).

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

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

$$2x-1=\log_{5}\left(26\right)$$

Adio 1 at ddwy ochr yr hafaliad.

$$2x=\log_{5}\left(26\right)-\left(-1\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\log_{5}\left(26\right)+1}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(5)}+\frac{\log_{5}\left(130\right)}{2}$$

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