Riješi {left(7/8right)}^2x+3=2

$${ \left( \frac{ 7 }{ 8 } \right) }^{ 2x+3 } =2$$

Riješite za x

$$x = -\frac{\log_{\frac{7}{8}} {(\frac{343}{1024})}}{2} \approx -4,095446535$$

Koraci pomoću definicije logaritma

Koristite pravila eksponenata i logaritama za rješavanje jednačine.

$$\left(\frac{7}{8}\right)^{2x+3}=2$$

Izračunajte logaritam obje strane jednačine.

$$\log(\left(\frac{7}{8}\right)^{2x+3})=\log(2)$$

Logaritam broja podignutog na stepen je stepen puta logaritam broja.

$$\left(2x+3\right)\log(\frac{7}{8})=\log(2)$$

Podijelite obje strane s \log(\frac{7}{8}).

$$2x+3=\frac{\log(2)}{\log(\frac{7}{8})}$$

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

$$2x+3=\log_{\frac{7}{8}}\left(2\right)$$

Oduzmite 3 s obje strane jednačine.

$$2x=\frac{\ln(2)}{\ln(\frac{7}{8})}-3$$

Podijelite obje strane s 2.

$$x=\frac{\frac{\ln(2)}{\ln(\frac{7}{8})}-3}{2}$$

Riješite za x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(\frac{7}{8})}-\frac{\log_{\frac{7}{8}}\left(\frac{343}{1024}\right)}{2}$$

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