9Math Q04-1001
Chapter 4
Logarithms
1. If the number 31200 is put in the form 3.12 ×10n, the value of n is
    A. 1    B. 2    C. 2    D. 4    E. 5
2. The scientific notation 3.5 ×103 multiplied by 3 is
    A. 1.05 ×102    B.1.05×1010    C. 1.05×103    D.1.05×109    E. 1.05×104
3. The scientific notation 8.2×10-4 + 5.4×10-4=………
    A.1.35×10-5    B. 1.36×10-4    C.1.36×10-3    D.1.36×10-7    E.1.36×103
4. Which of the following is (are) true?
    A.log⁡〖(xy) 〗=log⁡x + log⁡y    B.  (log⁡x )^n = n  log⁡x  C. log_10⁡1=0  
    D.log_x⁡x=1    E.log⁡(x/y)= log⁡x-log⁡y
5. Which of the following is (are) true?
    1.log⁡M/log⁡N =log⁡M-log⁡N       2.log⁡∛M=3 log⁡M        3.log_√a⁡M  =2log_a⁡M  
    A. 1 only   B. 2 only    C. 3 only    D. 1 and only    E. None of them
6.Which of the following is (are) true?
    1. log_4⁡x=2log_16⁡x         2. log_b⁡x=3 log_(b^3 )⁡x    3. log_4⁡16= log_16⁡4
    A. 1only    B. 2 only    C. 3 only    D. 1 and 2 only    E. 1 and 3 only
7.  〖10〗^(1+log_10⁡3 )=……..
    A.3    B.30    C. 3/10   D.10/3    E.15
8.(4)^log_2⁡3 =……..
    A.3    B.-6    C.9    D.12    E.15
9. log_3⁡5× log_25⁡27=………….
    A.3/2    B.2/3    C.5/27    D.3/25    E. 5×27
10.If x=log_b⁡a,y=log_c⁡b,z=log_a⁡c, then xyz=…………
    A. 0   B. 1   C.-1    D. abc    E. a+b+c
11. If log⁡2=a,  then =…….
    A.a^2    B.2.5a    C.1+a    D.1-a    E.1/2 a
12.If log⁡2=a, log⁡3=b, then log⁡144=………….
    A. a^4 b^2   B.4a+2b    C.8ab    D. a^2 b^2   E. None of them
13. 3+log_2⁡5=……..
    A.log_2⁡40    B.log_2⁡4    C.log_2⁡150    D. log_2⁡15   E.log_2⁡60
14. log⁡0.01=………
    A. 2   B. -2   C.1/2    D.-1/2    E.0
15. log_2⁡40+log_2⁡0.1+log_2⁡0.25=……….
    A. 0   B. 1   C.2    D. 3  E.4
16. log_2⁡〖2√2〗=………
    A. 2/3   B.1    C.1 1/2    D.-3/2    E.-2/3
17. log_(x-2)⁡(2x^2-10x+13)  =  1;   x=?
    A.-3    B.-5/2    C. 5/2   D. 2/5   E. 3 or5/2
18. If  log⁡2=m , then log_8⁡5 =………
    A. (1-m)/3m   B.1/3m    C. (3-m)/m   D. (1-m)^3   E.(3-m)/m
19.Solve  log⁡x×log⁡(12x+7) =1
    A. 1/3 (or) -2/3  B.  2/5 (or) 2/3   C.-5/4    D.2/3    E. 2/3 ( or) -5/4

20.If  log_10⁡x<0 , then 
    A. x<0   B.-1<x<0    C. -1<x<1    D. 0<x<1   E. x>1
21. If  log_10⁡x=0.35, then  log_10⁡√x=……….
    A. -1.75   B.-0.175    C. 0.175    D. 3.5    E. 0.7
22. Simplify  (log⁡√x+log⁡〖x^(3/2) 〗)/(4 log⁡√x )
    A.log⁡x    B.1    C.0    D.1/2  log⁡x    E.2
23. Solve the inequality  xlog_10⁡0.1>log_10⁡10.
    A. x<-1    B. x<1   C. x>1   D. x>100   E. x>-1
24. If  log⁡(p+q)= log⁡p-log⁡q , then p=……….
    A. p=q=1    B. p=q/(1-q)    C. p=q^2/(1-q)  D. p= q/(1+q)  E. p=q^2/(1+q)
25.If  log⁡a=5, log⁡b =3, then the value of  a/b  is
    A. 5/3   B. 2    C. 8   D. log⁡〖5/3〗   E.100
26. Given that  log_a⁡2 =0.301 and log_a⁡3 =0.477, then =……..
    A. 0.125   B. -0.125    C. 0.301   D. -1.125    E. 1.125
27. If 2log_p⁡8-log_p⁡4=2, then p=……….
    A. 4    B. -4   C. 4 (or) 2   D. 4 (or) -4    E. 2
28.  log_(1/9)⁡((x-1)/(x+2)) = 1/2; x=………
    A. 1/2   B. 3/2   C. 5/2   D.  7/2    E. 9/2
29.  log_3⁡(9^x-22)= x+2 ; x=…………
    A. log_11⁡3   B. log_3⁡11    C.log⁡3    D.log⁡11    E. 0
30.If  log⁡2=m, log⁡3=n,  then log⁡720 =……….
    A. m+n+1     B. 3m+n+1    C. 2m+3n+1    D. 3m+2n+1    E. 3m+2n-1 
31. log_2⁡9 =a ,  log_2⁡6=………..
    A. 1/(a+2)   B.(a+2)/2    C.  -a   D. a+1/2    E. 2a
32.   log⁡(0.04/0.4)=…….
    A.  -3   B. -2    C. -1    D. 1    E.4
33.  log_5⁡5+log_3⁡1+log_4⁡16=…….
    A. 0   B.  1  C. 2   D. 3   E.4
34. If  log⁡2.7 =0.431 , then  log⁡√2.7 =………
    A.1 ̅ .431   B.-0.215    C.0.2155    D. 0.862    E.-0.862
35.If  log⁡0.80 = 1 ̅.903 , then log⁡〖(0.80)^2 〗=…….
    A. 2 ̅.806   B. 3 ̅.806    C. 2 ̅.903  D. 1 ̅.806    E. 3 ̅.903
36. If  log⁡9=0.954 and  log⁡2 =0.310, then   log⁡1.8=…….
    A. 0.644   B. 1 ̅.264    C. 0.264    D. 2 ̅.264     E. -0.264
37.Given  log⁡40=1.602⁡〖(0.08)^(1/2) 〗=………
    A. 3 ̅.454    B. 2 ̅.454    C. 0.454   D. 1.454   E.  1 ̅.454
39.If  x^0.6=4, then  log_4⁡x=…….
    A. 3/5   B. 4    C. 5/3   D. -5/3   E.-3/5
40.   log_2⁡(4x-4)=2, then   log_2⁡x=…….
    A. 2   B. -2   C. 2/2   D. -1/2   E. 4

41. If  log⁡5=0.699, then the value of  log⁡500=……..
    A. 1.699   B. 2.699    C. 6.99    D. 69.9    E. 699
42.  log_a⁡2=0.301 ,  log_a⁡3=0.477, then  log_a⁡1.5 =…………..
    A. 0.778   B.0.176    C.0.602    D.0.954    E. None of them
43. If  log⁡5=0.699 and  log⁡x=0.233, then x=………….
    A. 3   B.5    C. 5^(1/3)   D. 5^(1/5)   E. 5/3 
44.  4 ̅.5-3 ̅.2=……….
    A. 1.3   B. -2.3    C. -3.3    D. 2 ̅.3    E.1 ̅ .3
45. If  log_10⁡x =0.35, then  log_√10⁡x =……….
    A. 0.175    B. 0.7    C. 3.5   D. 7.5   E.-0.175

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Thank you!