Datrys {left(1+3.2/100right)}^x=200

$${ \left(1+ \frac{ 3.2 }{ 100 } \right) }^{ x } =200$$

Datrys ar gyfer x

$$x=\log_{1.032}\left(200\right)\approx 168.207669123$$

Camau gan Ddefnyddio Diffiniad Logarithm

Ehangu \frac{3.2}{100} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\left(1+\frac{32}{1000}\right)^{x}=200$$

Lleihau'r ffracsiwn \frac{32}{1000} i'r graddau lleiaf posib drwy dynnu a chanslo allan 8.

$$\left(1+\frac{4}{125}\right)^{x}=200$$

Adio 1 a \frac{4}{125} i gael \frac{129}{125}.

$$\left(\frac{129}{125}\right)^{x}=200$$

Cymryd logarithm dwy ochr yr hafaliad.

$$\log(\left(\frac{129}{125}\right)^{x})=\log(200)$$

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

$$x\log(\frac{129}{125})=\log(200)$$

Rhannu’r ddwy ochr â \log(\frac{129}{125}).

$$x=\frac{\log(200)}{\log(\frac{129}{125})}$$

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

$$x=\log_{\frac{129}{125}}\left(200\right)$$

Datrys ar gyfer x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.032)}+\log_{1.032}\left(200\right)$$

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