Datrys 5^x2-5x+6=1

$${ 5 }^{ x2-5x+6 } =1$$

Datrys ar gyfer x

$$x=\frac{x_{2}+6}{5}$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{-5x+x_{2}+6}=1$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{-5x+x_{2}+6})=\log(1)$$

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

$$\left(-5x+x_{2}+6\right)\log(5)=\log(1)$$

Rhannu’r ddwy ochr â \log(5).

$$-5x+x_{2}+6=\frac{\log(1)}{\log(5)}$$

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

$$-5x+x_{2}+6=\log_{5}\left(1\right)$$

Tynnu x_{2}+6 o ddwy ochr yr hafaliad.

$$-5x=-\left(x_{2}+6\right)$$

Rhannu’r ddwy ochr â -5.

$$x=-\frac{x_{2}+6}{-5}$$

Datrys ar gyfer x_2

$$x_{2}=5x-6$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{x_{2}+6-5x}=1$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{x_{2}+6-5x})=\log(1)$$

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

$$\left(x_{2}+6-5x\right)\log(5)=\log(1)$$

Rhannu’r ddwy ochr â \log(5).

$$x_{2}+6-5x=\frac{\log(1)}{\log(5)}$$

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

$$x_{2}+6-5x=\log_{5}\left(1\right)$$

Tynnu -5x+6 o ddwy ochr yr hafaliad.

$$x_{2}=-\left(6-5x\right)$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{2\pi n_{1}i}{5\ln(5)}+\frac{x_{2}}{5}+\frac{6}{5}$$

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

Datrys ar gyfer x_2 (complex solution)

$$x_{2}=\frac{2\pi n_{1}i}{\ln(5)}+5x-6$$

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