1.             Then x = _______

 
2.  Simplify:   
 

3. The solutions of log ₁₀ (x²) = (log ₁₀ x)²  is/are
 

4. If log 2 = a  and  log 3 = b,  then log 120 is
 

5. log ₃₂ (1/64) =
 

6. If a = log ₈ 225  and  b = log ₂ 15 , then a in terms of b is
 

7. When simplified,     log 8      is
                               log (1/8)
 

8. If log ₁₀ n = 2.3456, which statement is true?

            a.  0 < n < 1          b.  2 < n < 3          c.  20 < n < 30
            d.  n > 100            e.  none of these

9. How many solutions are there to the equation  log x²  =  log x?
 
 

10.  log ₃ (log ₂ (log ₇ x)) = 0, then \/x  =
 

11.  Find:  (log ₅ 6)(log ₆ 7)(log ₇ 8)….(log ₁₂₄ 125)
 

12.  Find an integral solution for the equation    log _x-2 (x² + 2) = 3
 

13.   If a = log 2 and b = log 5, then log 20 =
 

14.  If a > 1, b > 1 and   , then a^p =
 

15.  How many real solutions are there to   3 ^{2x + 2} – 3 ^{x + 3} – 3^x + 3 = 0?
 

16.  If b > 1, sin x > 0, cos x > 0, and log _b sin x = 1, find log _b (cos x).
 

17.  (5 + (5 + 5^-1)^-1)^-1 =

      a.  25/5          b.  51/130          c.  26/135          d.  130/20          e.  16/25

Answers