Datrys 500=200*1.03^2x

$$500 = 200 \times 1.03 ^ { 2 x }$$

Datrys ar gyfer x

$$x = \frac{\log_{1.03} {(2.5)}}{2} \approx 15.499456378$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 200.

$$\frac{500}{200}=1.03^{2x}$$

Lleihau'r ffracsiwn \frac{500}{200} i'r graddau lleiaf posib drwy dynnu a chanslo allan 100.

$$\frac{5}{2}=1.03^{2x}$$

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

$$1.03^{2x}=\frac{5}{2}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.03^{2x})=\log(\frac{5}{2})$$

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

$$2x\log(1.03)=\log(\frac{5}{2})$$

Rhannu’r ddwy ochr â \log(1.03).

$$2x=\frac{\log(\frac{5}{2})}{\log(1.03)}$$

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

$$2x=\log_{1.03}\left(\frac{5}{2}\right)$$

Rhannu’r ddwy ochr â 2.

$$x=\frac{\ln(\frac{5}{2})}{2\ln(\frac{103}{100})}$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\pi n_{1}}{\ln(1.03)}+\frac{\log_{1.03}\left(2.5\right)}{2}$$

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