Riješi {left(1+32/100right)}^x=200

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

Riješite za x

$$x=\log_{\frac{33}{25}}\left(200\right)\approx 19,083975886$$

Koraci pomoću definicije logaritma

Svedite razlomak \frac{32}{100} na najprostije elemente rastavlјanjem i kraćenjem 4.

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

Saberite 1 i \frac{8}{25} da biste dobili \frac{33}{25}.

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

Izračunajte logaritam obje strane jednačine.

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

Logaritam broja podignutog na stepen je stepen puta logaritam broja.

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

Podijelite obje strane s \log(\frac{33}{25}).

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

Po formuli promjene osnove \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

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

Riješite za x (complex solution)

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

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