Given the simultaneous equations
2^x=3^y
x+y=1
show that x=log3/log6
2^x = 3^y ----(1)Originally Posted by kingkaisai2
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.