Datrys 50000=32000left(1+0.05right)^x

$$50000 = 32000 { \left( 1+0.05 \right) }^{ x }$$

Datrys ar gyfer x

$$x=2\log_{1.05}\left(1.25\right)\approx 9.147071141$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 32000.

$$\frac{50000}{32000}=\left(1+0.05\right)^{x}$$

Lleihau'r ffracsiwn \frac{50000}{32000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 2000.

$$\frac{25}{16}=\left(1+0.05\right)^{x}$$

Adio 1 a 0.05 i gael 1.05.

$$\frac{25}{16}=1.05^{x}$$

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

$$1.05^{x}=\frac{25}{16}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.05^{x})=\log(\frac{25}{16})$$

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

$$x\log(1.05)=\log(\frac{25}{16})$$

Rhannu’r ddwy ochr â \log(1.05).

$$x=\frac{\log(\frac{25}{16})}{\log(1.05)}$$

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

$$x=\log_{1.05}\left(\frac{25}{16}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.05)}+2\log_{1.05}\left(1.25\right)$$

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