Datrys 5000=30000*2^t

$$5000 = 30000 \cdot 2 ^ { t }$$

Datrys ar gyfer t

$$t=-\log_{2}\left(6\right)\approx -2.584962501$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 30000.

$$\frac{5000}{30000}=2^{t}$$

Lleihau'r ffracsiwn \frac{5000}{30000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 5000.

$$\frac{1}{6}=2^{t}$$

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

$$2^{t}=\frac{1}{6}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(2^{t})=\log(\frac{1}{6})$$

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

$$t\log(2)=\log(\frac{1}{6})$$

Rhannu’r ddwy ochr â \log(2).

$$t=\frac{\log(\frac{1}{6})}{\log(2)}$$

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

$$t=\log_{2}\left(\frac{1}{6}\right)$$

Datrys ar gyfer t (complex solution)

$$t=\frac{2\pi n_{1}i}{\ln(2)}-\log_{2}\left(6\right)$$

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