v9Math 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.-11 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 and log⁡30=1.477, then log⁡(40/3)=…….. A. 0.125 B. 1 ̅.125 C. 2.215 D. 1.125 E. None of these 38.Given that log⁡8=0.908 , then log⁡〖(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. 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