what is the constant in log2(x16y9) = Alogx +Blog2y such A=___ and the constant and B=__

You must apply the addition law of logarithm:

log_nab= log_na+log_nb

Then, 'transfer' any power to the front of the "log".

I won't do your work, here's an example:

log3(x^2y^3) = Alog3x + Blogy

log3(x^2y^3) = log3x^2y^3

OOOOOOOO= log3x^2 + logy^3

OOOOOOOO = 2log3x + 3logy

By comparing the coefficients of log(3x) and log(y), you can find the A and B to be 2 and 3 respectively in my example.

Try with your question and post back your answer. :)