Datrys 5^3x-7=25

$$5 ^ { 3 x - 7 } = 25$$

Datrys ar gyfer x

$$x=3$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$5^{3x-7}=25$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{3x-7})=\log(25)$$

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

$$\left(3x-7\right)\log(5)=\log(25)$$

Rhannu’r ddwy ochr â \log(5).

$$3x-7=\frac{\log(25)}{\log(5)}$$

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

$$3x-7=\log_{5}\left(25\right)$$

Adio 7 at ddwy ochr yr hafaliad.

$$3x=2-\left(-7\right)$$

Rhannu’r ddwy ochr â 3.

$$x=\frac{9}{3}$$

Datrys ar gyfer x (complex solution)

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

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