Question

URGENTE!!
Se log2 x = p, com x > 0, então, log2 x + log4 x^3 é igual a:

Answer 1

$\log_2 x=p$

$\log_2 x+\log_4 x^3=$

$p+\frac{\log x^3}{\log 4}=$

$p+\frac{\log x^3}{\log 2^2}=$

$p+\frac{3\log x}{2\log 2}=$

$p+\frac{3}{2}\cdot \frac{\log x}{\log 2}=$

$p+\frac{3}{2}\cdot \log_2 x=$

$p+\frac{3}{2}\cdot p=$

$p+\frac{3p}{2}=$

$\frac{2p}{2}+\frac{3p}{2}=$

$\frac{5p}{2}$

Concluímos então que $\log_2 x+\log_4 x^3= \frac{5p}{2}$