Find the value of x in: log (base a) x = 3/2 log (base a) 9 + log (base a) 9?

since the bases are all the same you can ignore them and just say x=(3/2) times 9 + 9

log is log to base a in the following : -
log x = (3/2) log 9 + log 9
log x = (5/2) log 9
log x = log 9^(5/2)
x = 9^(5/2)
x = 3^5
x = 243

k log (base a) = m
=> log (base a) a^ k =m

log (base a)x = (3/2) log (base a)9 + log (base a)9
log (base a)x = (5/2) log (base a)9
log (base a)x = log (base a)9^(5/2)
x = 9^(5/2)
x = 3^2^(5/2)
x = 243

x = 9 ^(3/2) * 9
= 9^(5/2)
= 3^(2 * 5 /2)
= 3^5