Max.....I assume you want this in terms of x and y instead of a and b
x = log2 3 y = log3 7 log42 56 use the change of base rule to write :
x = log 3 / log 2 → log 2 = log 3/ x
y = log 7 / log 3 → log 7 = y log 3
log42 56 = log 56 / log 42 and we can write this as :
log ( 2^3 * 7 ) / log ( 2 * 7 * 3) =
[log2^3 + log 7] / [ log 2 + log 7 + log 3] =
[3 log 2 + y log 3 ] / [ log3 / x + y log 3 + log 3]
[ 3 * (log 3)/x + y log 3 ] / [ log 3/x + ylog 3 + log 3] = [multiply top/bottom by x]
[ 3 log 3 + xylog3 ] / [ log 3 + xylog 3 + x log 3] = factor out log 3
[ (log 3) ( 3 + xy ) ] / [ (log 3) [ 1 + xy + x ] =
[ 3 + xy ] / [ 1 + xy + x ]