Question

Se log102 = m e log₁03 = n, podemos afirmar que o log56 é:

A) 2mn/ 1-m

B) M+n/ 1+m

C) M+n/ mn

D) M+n/ 1-m

E) 3mn/ 1+m

Me ajudem por favor, isso é urgente!!!

Façam a boa aí, é a última questão por favor

Answer 1

$\large\boxed{\begin{array}{l}\rm Se\,\ell og_{10}2=m\,e\,\ell og_{10}3=n,podemos\\\rm afirmar\,que\,o\,\ell og_56\,\acute e:\\\rm A)~\dfrac{2mn}{1-m}\\\\\rm B)~\dfrac{m+n}{1+m}\\\\\rm C)~\dfrac{m+n}{mn}\\\\\rm D)~\dfrac{ m+n}{1-m}\,\blacksquare\\\\\rm E)~\dfrac{3mn}{1+m}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\boldsymbol{soluc_{\!\!,}\tilde ao\!:}}\\\sf \ell og_56=\dfrac{\ell og6}{\ell og5}\\\sf\ell og5=\ell og\bigg(\dfrac{10}{2}\bigg)=\ell og10-\ell og2=1-m\\\sf \ell og6=\ell og(2\cdot3)=\ell og2+\ell og3=m+n\\\underline{\rm substituindo\,temos:}\\\sf\ell og_56=\dfrac{m+n}{1-m}\end{array}}$