Given that \(2^{x} = 9\) and \(27^{y} = 2\) find the value of \(xy\).
2^x = 9
27^y = 2
Rewrite as
x = log 9/log 2 = log 3^2 / log 2 = 2log 3 / log 2
y = log 2 / log 27 = log 2 / log 3^3 = log 2 / {3 log 3 ]
So
xy = 2log 3 / log 2 * log 2 / [ 3 log 3 ] = 2/3
