Datrys 2500=1500(1+.06)^x

$$2500 = 1500 ( 1 + .06 ) ^ { x }$$

Datrys ar gyfer x

$$x=\log_{1.06}\left(\frac{5}{3}\right)\approx 8.766692911$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 1500.

$$\frac{2500}{1500}=\left(1+0.06\right)^{x}$$

Lleihau'r ffracsiwn \frac{2500}{1500} i'r graddau lleiaf posib drwy dynnu a chanslo allan 500.

$$\frac{5}{3}=\left(1+0.06\right)^{x}$$

Adio 1 a 0.06 i gael 1.06.

$$\frac{5}{3}=1.06^{x}$$

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

$$1.06^{x}=\frac{5}{3}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.06^{x})=\log(\frac{5}{3})$$

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

$$x\log(1.06)=\log(\frac{5}{3})$$

Rhannu’r ddwy ochr â \log(1.06).

$$x=\frac{\log(\frac{5}{3})}{\log(1.06)}$$

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

$$x=\log_{1.06}\left(\frac{5}{3}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.06)}+\log_{1.06}\left(\frac{5}{3}\right)$$

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