Resolver =-[2/10b_{2}(2/10)+8/10log_{2}(8/10)]

$$= - [ \frac { 2 } { 10 } b _ { 2 } ( \frac { 2 } { 10 } ) + \frac { 8 } { 10 } \log _ { 2 } ( \frac { 8 } { 10 } ) ]$$

Calcular

$$-\frac{b_{2}}{25}+\frac{4\log_{2}\left(5\right)}{5}-\frac{8}{5}$$

Pasos da solución

Multiplica \frac{2}{10} e \frac{2}{10} para obter \left(\frac{2}{10}\right)^{2}.

$$-\left(\left(\frac{2}{10}\right)^{2}b_{2}+\frac{8}{10}\log_{2}\left(\frac{8}{10}\right)\right)$$

Reduce a fracción \frac{2}{10} a termos máis baixos extraendo e cancelando 2.

$$-\left(\left(\frac{1}{5}\right)^{2}b_{2}+\frac{8}{10}\log_{2}\left(\frac{8}{10}\right)\right)$$

Calcula \frac{1}{5} á potencia de 2 e obtén \frac{1}{25}.

$$-\left(\frac{1}{25}b_{2}+\frac{8}{10}\log_{2}\left(\frac{8}{10}\right)\right)$$

Reduce a fracción \frac{8}{10} a termos máis baixos extraendo e cancelando 2.

$$-\left(\frac{1}{25}b_{2}+\frac{4}{5}\log_{2}\left(\frac{8}{10}\right)\right)$$

Reduce a fracción \frac{8}{10} a termos máis baixos extraendo e cancelando 2.

$$-\left(\frac{1}{25}b_{2}+\frac{4}{5}\log_{2}\left(\frac{4}{5}\right)\right)$$

Para calcular o oposto de \frac{1}{25}b_{2}+\frac{4}{5}\log_{2}\left(\frac{4}{5}\right), calcula o oposto de cada termo.

$$-\frac{1}{25}b_{2}-\frac{4}{5}\log_{2}\left(\frac{4}{5}\right)$$

Factorizar

$$\frac{-b_{2}+20\log_{2}\left(5\right)-40}{25}$$

Pasos da solución

Considera \frac{1}{5}\times \frac{1}{5}b_{2}+\frac{4}{5}\ln(\frac{4}{5})\ln(2)^{-1}. Factoriza \frac{1}{25}.

$$\frac{b_{2}+20\log_{2}\left(\frac{4}{5}\right)}{25}$$

Reescribe a expresión factorizada completa. Simplifica.

$$-\frac{b_{2}+20\log_{2}\left(\frac{4}{5}\right)}{25}$$