Interpreting this as [2xlog2] / [xlog3]=log2 multiply both sides by x log3 and divide both sides by log2
[ 2x log 2] / [log 2 ] = x log 3 simplify
2x = x log 3 subtract log 3 from both sides
2x - x log 3 = 0 factor
x (2 - log 3 ) = 0 so x = 0
But x cannot = 0 because it makes the denominator on the LHS of the original problem undefined....so this has no solution.....
Interpreting this as [2xlog2] / [xlog3]=log2 multiply both sides by x log3 and divide both sides by log2
[ 2x log 2] / [log 2 ] = x log 3 simplify
2x = x log 3 subtract log 3 from both sides
2x - x log 3 = 0 factor
x (2 - log 3 ) = 0 so x = 0
But x cannot = 0 because it makes the denominator on the LHS of the original problem undefined....so this has no solution.....