Datrys 8*31^x=80

$$8 \times 31 ^ { x } = 80$$

Datrys ar gyfer x

$$x=\log_{31}\left(10\right)\approx 0.670528152$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$8\times 31^{x}=80$$

Rhannu’r ddwy ochr â 8.

$$31^{x}=10$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(31^{x})=\log(10)$$

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

$$x\log(31)=\log(10)$$

Rhannu’r ddwy ochr â \log(31).

$$x=\frac{\log(10)}{\log(31)}$$

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

$$x=\log_{31}\left(10\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(31)}+\log_{31}\left(10\right)$$

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