Sol. The given inequality is

( +1) log 5 + ( + 1) ≤ 0 …(1)

The inequality (1) consists of all x satisfying the system

i.e. the system

It follows that domain consists of all x satisfying the system

⇒ {x = 1, 3

Let x = 1, substituting this value into the left hand side of inequality (1), we obtain

log 5 + 1 = –1 + 1 = 0, i.e. the value x = 1 is its solution.

Let x = 3. Then the left hand-side of the initial inequality is equal to

log 5 + = log 5 3 –1 + = log 5 3 –

= log 5

Since 27 > 25; it follows that 3 > 5 2/3 , i.e. > 1 and consequently > 0.

Therefore, the value x = 3 is not a solution of the initial inequality.

Thus the set of solutions of the initial inequality consists of a single number x = 1.