Datrys 9600=4800(1+5*5/100)^x

$$9600 = 4800 ( 1 + 5 \cdot 5 / 100 ) ^ { x }$$

Datrys ar gyfer x

$$x=\log_{\frac{5}{4}}\left(2\right)\approx 3.10628372$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 4800.

$$\frac{9600}{4800}=\left(1+5\times \frac{5}{100}\right)^{x}$$

Rhannu 9600 â 4800 i gael 2.

$$2=\left(1+5\times \frac{5}{100}\right)^{x}$$

Lleihau'r ffracsiwn \frac{5}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 5.

$$2=\left(1+5\times \frac{1}{20}\right)^{x}$$

Lluosi 5 a \frac{1}{20} i gael \frac{1}{4}.

$$2=\left(1+\frac{1}{4}\right)^{x}$$

Adio 1 a \frac{1}{4} i gael \frac{5}{4}.

$$2=\left(\frac{5}{4}\right)^{x}$$

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

$$\left(\frac{5}{4}\right)^{x}=2$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{5}{4}\right)^{x})=\log(2)$$

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

$$x\log(\frac{5}{4})=\log(2)$$

Rhannu’r ddwy ochr â \log(\frac{5}{4}).

$$x=\frac{\log(2)}{\log(\frac{5}{4})}$$

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

$$x=\log_{\frac{5}{4}}\left(2\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{5}{4})}+\log_{\frac{5}{4}}\left(2\right)$$

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