Prove: log base A x - log base A y = log base A ( x/y)

Answer 1

x = A^{log A x}

y = A^{log A y}

x/y = A^{log A x} / A^{log A y}

x/y = A^{(log A x - log A y)}

log _A (x/y) = log_A x - log_{A y}

QED