Question

$log_{7+4sqrt3}7-4sqrt3=?$

Answer 1

log(7+4√3) (7-4√3) = log(7+4√3) (7-4√3) +1 -1 =
=  log(7+4√3) (7-4√3) +log(7+4√3) (7+4√3) -1 =
=  log(7+4√3) (7-4√3)(7+4√3) -1 =
=  log(7+4√3) (7^2 -16*3) -1 =
=  log(7+4√3) (49 -48) -1 =
=  log(7+4√3) 1 -1 =
= 0 -1 = -1