Datrys 14.400=4000(1.025)^x

$$14.400 = 4000 ( 1.025 ) ^ { x }$$

Datrys ar gyfer x

$$x=2\log_{1.025}\left(0.06\right)\approx -227.874689765$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 4000.

$$\frac{14.4}{4000}=1.025^{x}$$

Ehangu \frac{14.4}{4000} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\frac{144}{40000}=1.025^{x}$$

Lleihau'r ffracsiwn \frac{144}{40000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 16.

$$\frac{9}{2500}=1.025^{x}$$

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

$$1.025^{x}=\frac{9}{2500}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.025^{x})=\log(\frac{9}{2500})$$

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

$$x\log(1.025)=\log(\frac{9}{2500})$$

Rhannu’r ddwy ochr â \log(1.025).

$$x=\frac{\log(\frac{9}{2500})}{\log(1.025)}$$

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

$$x=\log_{1.025}\left(\frac{9}{2500}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.025)}+2\log_{1.025}\left(0.06\right)$$

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