**find x if x is an integer and 40<log 4 64^x<45**

**Answer:**

First note that log4 64^x is equal to x*(log4 64).

Next this equals x*3 (Because 64 = 4^3).

So we need to find an integer x such that 40 < 3x <45.

i.e. 40/3 < x < 45/3

i.e. 13.33 < x < 15

So x = 14.