Datrys 20=50(.92)^x

$$20 = 50 ( .92 ) ^ { x }$$

Datrys ar gyfer x

$$x=\log_{0.92}\left(0.4\right)\approx 10.989122704$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 50.

$$\frac{20}{50}=0.92^{x}$$

Lleihau'r ffracsiwn \frac{20}{50} i'r graddau lleiaf posib drwy dynnu a chanslo allan 10.

$$\frac{2}{5}=0.92^{x}$$

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

$$0.92^{x}=\frac{2}{5}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(0.92^{x})=\log(\frac{2}{5})$$

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

$$x\log(0.92)=\log(\frac{2}{5})$$

Rhannu’r ddwy ochr â \log(0.92).

$$x=\frac{\log(\frac{2}{5})}{\log(0.92)}$$

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

$$x=\log_{0.92}\left(\frac{2}{5}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(0.92)}+\log_{0.92}\left(0.4\right)$$

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