Datrys {left(1+32/100right)}^x=200

$${ \left(1+ \frac{ 32 }{ 100 } \right) }^{ x } =200$$

Datrys ar gyfer x

$$x=\log_{\frac{33}{25}}\left(200\right)\approx 19.083975886$$

Camau gan Ddefnyddio Diffiniad Logarithm

Lleihau'r ffracsiwn \frac{32}{100} i'r graddau lleiaf posib drwy dynnu a chanslo allan 4.

$$\left(1+\frac{8}{25}\right)^{x}=200$$

Adio 1 a \frac{8}{25} i gael \frac{33}{25}.

$$\left(\frac{33}{25}\right)^{x}=200$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{33}{25}\right)^{x})=\log(200)$$

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

$$x\log(\frac{33}{25})=\log(200)$$

Rhannu’r ddwy ochr â \log(\frac{33}{25}).

$$x=\frac{\log(200)}{\log(\frac{33}{25})}$$

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

$$x=\log_{\frac{33}{25}}\left(200\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(\frac{33}{25})}+\log_{\frac{33}{25}}\left(200\right)$$

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