Datrys 20000=7000{(e)^20x}

$$20000=7000 {(e)^{ 20x }}$$

Datrys ar gyfer x

$$x=\frac{\ln(\frac{20}{7})}{20}\approx 0.052491106$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 7000.

$$\frac{20000}{7000}=e^{20x}$$

Lleihau'r ffracsiwn \frac{20000}{7000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 1000.

$$\frac{20}{7}=e^{20x}$$

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

$$e^{20x}=\frac{20}{7}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(e^{20x})=\log(\frac{20}{7})$$

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

$$20x\log(e)=\log(\frac{20}{7})$$

Rhannu’r ddwy ochr â \log(e).

$$20x=\frac{\log(\frac{20}{7})}{\log(e)}$$

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

$$20x=\log_{e}\left(\frac{20}{7}\right)$$

Rhannu’r ddwy ochr â 20.

$$x=\frac{\ln(\frac{20}{7})}{20}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{\pi n_{1}i}{10}+\frac{\ln(\frac{20}{7})}{20}$$

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