Verified answer

clarity is all important in mathematics....will assume you have log { base 3} √3 , which equals [1/2] = 2^(-1)

The log base 3 of sqrt(3) is 1/2, not -2. You can get there by doing

log_3 sqrt(3) = log_3 3^(1/2) = (1/2) log_3 3 = 1/2

If this is not what you meant, please write more clearly.