Find x if x is an integer and 40<log4 64^x<45

40log4-64x45

#1

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.