Datrys 20=50(92)^x

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

Datrys ar gyfer x

$$x=\log_{92}\left(\frac{2}{5}\right)\approx -0.202639004$$

Camau gan Ddefnyddio Diffiniad Logarithm

Rhannu’r ddwy ochr â 50.

$$\frac{20}{50}=92^{x}$$

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

$$\frac{2}{5}=92^{x}$$

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

$$92^{x}=\frac{2}{5}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(92^{x})=\log(\frac{2}{5})$$

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

$$x\log(92)=\log(\frac{2}{5})$$

Rhannu’r ddwy ochr â \log(92).

$$x=\frac{\log(\frac{2}{5})}{\log(92)}$$

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

$$x=\log_{92}\left(\frac{2}{5}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(92)}+\log_{92}\left(\frac{2}{5}\right)$$

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