If 3 log 4 (a-2) = (9/2), what is a?

First, we'll divide by 3 both
sides:

log4(a-2) = 9/2*3

We'll simplify
and we'll get:

log4(a-2) = 3/2

Now,
we'll use the property:

log a (b) = c => b =
a^c

We'll put a = 4, b = a-2 and c =
3/2

log4(a-2) = 3/2 <=> a - 2 =
4^(3/2)

But 4 = 2^2

a - 2 =
2^3

a - 2 = 8

a = 8 +
2

a = 10