Question

Se log 2= a e log 3 = b, qual é o valor de log 72 em função de a e b?????

Answer 1

$\mathrm{\ell og\,}2=a\;\;\text{ e }\;\;\mathrm{\ell og\,}3=b$


$\mathrm{\ell og\,}72=\mathrm{\ell og\,}(2^{3}\cdot 3^{2})\\ \\ \mathrm{\ell og\,}72=\mathrm{\ell og\,}(2^{3})+\mathrm{\ell og\,}(3^{2})\\ \\ \mathrm{\ell og\,}72=3\mathrm{\,\ell og\,}2+2\mathrm{\,\ell og\,}3\\ \\ \mathrm{\ell og\,}72=3a+2b$