Datrys 47000000div9428=123^x

$$47000000 \div 9428 = { 123 }^{ x }$$

Datrys ar gyfer x

$$x=\log_{123}\left(\frac{11750000}{2357}\right)\approx 1.769304388$$

Camau gan Ddefnyddio Diffiniad Logarithm

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

$$\frac{11750000}{2357}=123^{x}$$

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

$$123^{x}=\frac{11750000}{2357}$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(123^{x})=\log(\frac{11750000}{2357})$$

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

$$x\log(123)=\log(\frac{11750000}{2357})$$

Rhannu’r ddwy ochr â \log(123).

$$x=\frac{\log(\frac{11750000}{2357})}{\log(123)}$$

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

$$x=\log_{123}\left(\frac{11750000}{2357}\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(123)}+\log_{123}\left(\frac{11750000}{2357}\right)$$

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