Datrys 450=130{(e)^-71(x)}

$$450=130 {(e)^{ -71(x) }}$$

Datrys ar gyfer x

$$x=\frac{\ln(\frac{13}{45})}{71}\approx -0.017488917$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 130.

$$\frac{450}{130}=e^{-71x}$$

Lleihau'r ffracsiwn \frac{450}{130} i'r graddau lleiaf posib drwy dynnu a chanslo allan 10.

$$\frac{45}{13}=e^{-71x}$$

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

$$e^{-71x}=\frac{45}{13}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{-71x})=\log(\frac{45}{13})$$

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

$$-71x\log(e)=\log(\frac{45}{13})$$

Rhannu’r ddwy ochr â \log(e).

$$-71x=\frac{\log(\frac{45}{13})}{\log(e)}$$

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

$$-71x=\log_{e}\left(\frac{45}{13}\right)$$

Rhannu’r ddwy ochr â -71.

$$x=\frac{\ln(\frac{45}{13})}{-71}$$

Datrys ar gyfer x (complex solution)

$$x=-\frac{2\pi n_{1}i}{71}+\frac{\ln(\frac{13}{45})}{71}$$

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