Datrys 5^2x-3+5^2=26

$${ 5 }^{ 2x-3 } + { 5 }^{ 2 } =26$$

Datrys ar gyfer x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{2x-3}+25=26$$

Tynnu 25 o ddwy ochr yr hafaliad.

$$5^{2x-3}=1$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{2x-3})=\log(1)$$

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

$$\left(2x-3\right)\log(5)=\log(1)$$

Rhannu’r ddwy ochr â \log(5).

$$2x-3=\frac{\log(1)}{\log(5)}$$

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

$$2x-3=\log_{5}\left(1\right)$$

Adio 3 at ddwy ochr yr hafaliad.

$$2x=-\left(-3\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{3}{2}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(5)}+\frac{3}{2}$$

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