2^x = 3^y ----(1)Originally Posted bykingkaisai2

x +y = 1 ---------(2)

Take the logs of both sides of (1),

x*log(2) = y*log(3) ----(1a)

From (2),

y = 1-x

Substitute that into (1a),

x*log(2) = (1-x)log(3)

x*log(2) = log(3) -x*log(3)

x*log(2) +x*log(3) = log(3)

x[log(2) +log(3)] = log(3)

x[log(2*3)] = log(3)

x*log(6) = log(3)

x = log(3) / log(6) ---------answer.