Resolução:
[tex3]\log 432+\log 648=p+q[/tex3]
[tex3]\log (432\cdot 648)=p+q[/tex3]
Mas [tex3]432=2^{4}\cdot 3^{3}\,\,\,\text{ e }\,\,\,\,648=2^{3}\cdot 3^{4}[/tex3]
[tex3]\log (2^{4}\cdot 3^{3})(2^{3}\cdot 3^{4})=p+q[/tex3]
[tex3]\log (2^{4}\cdot 2^{3})(3^{3}\cdot 3^{4})=p+q[/tex3]
[tex3]\log 2^{7}\cdot 3^{7}=p+q[/tex3]
[tex3]\log (2\cdot 3)^{7}=p+q[/tex3]
[tex3]7\log 6=p+q[/tex3]
[tex3]\therefore \log 6=\frac{p+q}{7}[/tex3]