Datrys 5=(1+9.6%)^n

$$5 = ( 1 + 9.6 \% ) ^ { n }$$

Datrys ar gyfer n

$$n=\log_{1.096}\left(5\right)\approx 17.557404545$$

Camau gan Ddefnyddio Diffiniad Logarithm

Ehangu \frac{9.6}{100} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$5=\left(1+\frac{96}{1000}\right)^{n}$$

Lleihau'r ffracsiwn \frac{96}{1000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 8.

$$5=\left(1+\frac{12}{125}\right)^{n}$$

Adio 1 a \frac{12}{125} i gael \frac{137}{125}.

$$5=\left(\frac{137}{125}\right)^{n}$$

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

$$\left(\frac{137}{125}\right)^{n}=5$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{137}{125}\right)^{n})=\log(5)$$

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

$$n\log(\frac{137}{125})=\log(5)$$

Rhannu’r ddwy ochr â \log(\frac{137}{125}).

$$n=\frac{\log(5)}{\log(\frac{137}{125})}$$

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

$$n=\log_{\frac{137}{125}}\left(5\right)$$