Datrys 25=510(5)^x

$$25 = 510 ( 5 ) ^ { x }$$

Datrys ar gyfer x

$$x=-\log_{5}\left(102\right)+1\approx -1.87365718$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 510.

$$\frac{25}{510}=5^{x}$$

Lleihau'r ffracsiwn \frac{25}{510} i'r graddau lleiaf posib drwy dynnu a chanslo allan 5.

$$\frac{5}{102}=5^{x}$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$5^{x}=\frac{5}{102}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(5^{x})=\log(\frac{5}{102})$$

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

$$x\log(5)=\log(\frac{5}{102})$$

Rhannu’r ddwy ochr â \log(5).

$$x=\frac{\log(\frac{5}{102})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{5}{102}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(5)}+\log_{5}\left(\frac{5}{102}\right)$$

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