log₉ 8 = P, log₉ 12 = Q, log₉ 11 = R, Find log₉ 3/4

Answer 1

3/4 = 9/12, so we can write:

log₉(3/4) = log₉(9/12)

Now use the log property that log(a/b) = log(a) - log(b):

log₉(3/4) = log₉(9/12) = log₉(9) - log₉(12)

Now use the identity log₉(9) = 1 and the given value of log₉(12) = Q:

log₉(3/4) = log₉(9/12) = log₉(9) - log₉(12) = 1 - Q