TMUAmockz Set 1 Paper 2 · Question 12

A student claims that $\log_3(x-4)+\log_3(22-x)<4$ holds for all integers $x$ with $4<x<22$ . Is the student correct? If not, state the integer values for which the inequality fails and find the total number of integers with $4<x<22$ for which it does hold.

AThe student is correct; all 17 integers satisfy the inequality

BThe student is incorrect; the inequality fails for

x=4

and

x=22

only

CThe student is incorrect; the inequality fails for 2 integers

DThe student is incorrect; the inequality fails for exactly 1 integer, giving 16 valid values

EThe student is incorrect; the inequality fails for 3 integers

FThe student is incorrect; the inequality fails for 4 integers

examday

TMUAmockz Set 1 Paper 2 · Q12