Question

Log2 16-log4 32 é igual a?

Answer 1

$\log_{2}16-\log_{4}32$

$\log_{2} 2^{4} - \dfrac{\log_{2}32}{\log_{2}4}$

$4\log_{2} 2 - \dfrac{\log_{2} 2^{5} }{\log_{2} 2^{2} }$

$4.1 - \dfrac{5.\log_{2} 2 }{2.\log_{2} 2}$

$4 - \dfrac{5.1 }{2.1}$

$4 - \dfrac{5 }{2}$

$\dfrac{8-5 }{2}$

$\dfrac{3 }{2}$

Answer 2

$\log_2(16)-\log_4(32)$

$4=2^2$

$\log_2(16)-\log_{2^2}(32)$

$16=2^4~~~~e~~~~32=2^5$

$\log_2(2^4)-\log_{2^2}(2^5)$

o expoente da base passa dividindo e o do logaritmando passa multiplicando o log

$4\log_2(2)-\frac{1}{2}*5\log_2(2)$

Sabemos que:

$log_a(a)=1$

então

$4-\frac{5}{2}$

Fazendo o MMC

$\boxed{\boxed{\log_2(16)-\log_4(32)=\frac{3}{2}}}$