Datrys 3*{485}^frac{x{10}}=4000

$$3 \times { 485 }^{ \frac{ x }{ 10 } } = 4000$$

Datrys ar gyfer x

$$x=-10\log_{485}\left(\frac{3}{4000}\right)\approx 11.635291256$$

Camau gan Ddefnyddio Diffiniad Logarithm

Defnyddio rheolau esbonyddion a logarithmau i ddatrys yr hafaliad.

$$3\times 485^{\frac{1}{10}x}=4000$$

Rhannu’r ddwy ochr â 3.

$$485^{\frac{1}{10}x}=\frac{4000}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(485^{\frac{1}{10}x})=\log(\frac{4000}{3})$$

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

$$\frac{1}{10}x\log(485)=\log(\frac{4000}{3})$$

Rhannu’r ddwy ochr â \log(485).

$$\frac{1}{10}x=\frac{\log(\frac{4000}{3})}{\log(485)}$$

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

$$\frac{1}{10}x=\log_{485}\left(\frac{4000}{3}\right)$$

Lluosi’r ddwy ochr â 10.

$$x=\frac{\ln(\frac{4000}{3})}{\frac{1}{10}\ln(485)}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{20\pi n_{1}i}{\ln(485)}-10\log_{485}\left(\frac{3}{4000}\right)$$

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