Question 709692
{{{(log( 3, (7 )))(log( 4, (3 )))(log( 7, (6 )))}}}
The only way to combine logs is if they have the same base. So we will be working with the change of base formula, {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}, to match up the bases of the logarithms we've been given.<br>
Seeing that the base of the first log matches the base of the 2nd log, I see good things happening if we start by changing the base of the first log from 7 to 4 (so it matches the base of the second log):
{{{(log( 4, (7 ))/log(4, (3)))(log( 4, (3 )))(log( 7, (6 )))}}}
The base 4 logs of 3 cancel leaving:
{{{(log( 4, (7 )))(log( 7, (6 )))}}}
Again we have logs where the base of one is the same as the argument of the other. So I'll change the base of the second log from 7 to 4:
{{{(log( 4, (7 )))(log( 4, (6 ))/log(4, (7)))}}}
The base 4 logs of 7 cancel leaving:
{{{log( 4, (6 ))}}}