Datrys 47000000div9428=1.23^x

$$47000000 \div 9428 = { 1.23 }^{ x }$$

Datrys ar gyfer x

$$x=\log_{1.23}\left(\frac{11750000}{2357}\right)\approx 41.128676945$$

Camau gan Ddefnyddio Diffiniad Logarithm

Lleihau'r ffracsiwn \frac{47000000}{9428} i'r graddau lleiaf posib drwy dynnu a chanslo allan 4.

$$\frac{11750000}{2357}=1.23^{x}$$

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

$$1.23^{x}=\frac{11750000}{2357}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(1.23^{x})=\log(\frac{11750000}{2357})$$

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

$$x\log(1.23)=\log(\frac{11750000}{2357})$$

Rhannu’r ddwy ochr â \log(1.23).

$$x=\frac{\log(\frac{11750000}{2357})}{\log(1.23)}$$

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

$$x=\log_{1.23}\left(\frac{11750000}{2357}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.23)}+\log_{1.23}\left(\frac{11750000}{2357}\right)$$

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