Question

se log2-a e log3=b coloque em função de a e b os seguintes logaritimos decimais 
a)log 12               b)log 0,5               c)log 4

Answer 1

a)

$log~12=log~(3\cdot2\cdot2)\\log~12=log~3+log~2+log~2\\log~12=b+a+a\\\\\boxed{\boxed{log~12=2a+b}}$

b)

$log~0,5=log~\left(\frac{1}{2}\right)\\log~0,5=log~(2^{-1})\\log~0,5=(-1)\cdot log~2\\log~0,5=(-1)\cdot a\\\\\boxed{\boxed{log~0,5=-a}}$

c)

$log~4=log~(2^{2})\\log~4=2\cdot log~2\\log~4=2\cdot a\\\\\boxed{\boxed{log~4=2a}}$

Answer 2

a)log 12 ==> log (2².3) ==> log 2² + log 3 ==> 2log2 + log3 ==> a + b

b)log 0,5 ==> log 5/10 ==> log 1/2 ==> log 1 - log 2 ==> 0 - a ==> - a
    
Por definição log1 = 0
                                             ou 

log 0,5 ==> log 5/10 ==> log 1/2 ==> log 2^(-1) ==> -1log2 ==> -1.a ==> - a
                      
c)log 4 ==> log 2²  ==> 2log2 ==> 2a