Datrys 100=325(1-0.29)^t

$$100 = 325 ( 1 - 0.29 ) ^ { t }$$

Datrys ar gyfer t

$$t=\log_{0.71}\left(\frac{4}{13}\right)\approx 3.441425832$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 325.

$$\frac{100}{325}=\left(1-0.29\right)^{t}$$

Lleihau'r ffracsiwn \frac{100}{325} i'r graddau lleiaf posib drwy dynnu a chanslo allan 25.

$$\frac{4}{13}=\left(1-0.29\right)^{t}$$

Tynnu 0.29 o 1 i gael 0.71.

$$\frac{4}{13}=0.71^{t}$$

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

$$0.71^{t}=\frac{4}{13}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(0.71^{t})=\log(\frac{4}{13})$$

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

$$t\log(0.71)=\log(\frac{4}{13})$$

Rhannu’r ddwy ochr â \log(0.71).

$$t=\frac{\log(\frac{4}{13})}{\log(0.71)}$$

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

$$t=\log_{0.71}\left(\frac{4}{13}\right)$$