Exercise # 4 [Subjective Type Questions] log a N = 1 + loga b & indicate the permissible values of the letters. log ab N 1. Prove that 2. The positive integers p, q and r are all primes if p2 – q2 = r, then find all possible values of r. 3. Solve the system of equations : loga x loga (xyz) = 48 loga y loga (xyz) = 12, a > 0, a  1 loga z loga (xyz) = 84 a c e 2 a 4 b 2  3a 2 c2  5e 4 f = = , then find the value of in terms of a and b. b d f 2 b6  3b 2 d 2  5f 5 4. If 5. Given a 2  b 2  c 2 & a > 0 ; b >0 ; c >0 , c – b  1, c +b  1, Prove that : logc+b a + logc–b a = 2 . logc+b a . logc–b a 6. Solve the simultaneous equations |x + 2| + y = 5, x – |y| = 1 7. Find a rational number which is 50 times its own logarithm to the base 10. 8. Solve the equations log100 |x + y| = 1/2 , log10y – log10|x| = log1004 for x and y. 9. 1   Solve for x : log 4   1   log 3  log  x 3  27  .  2x  10. Find the values of x satisfying the equation x  1A = (x  1)7 , where A = log3 x²  2 logx 9. 11. Solve the following equation for x & y : log100 x  y  12. Find the real values of x and y for which the following equation is satisfied : 1 , log10y – log10|x|= log1004. 2 (1  i) x  2i (2  3i) y  i + =i 3i 3i 13. If the numbers 296, 436 and 542 divided by a positive number 'p' leaving the remainder 7, 11 and 15 respectively, then find the largest value of p. 14. Solve the following inequalities : (iii) 4x  6 0 x log2x  log x + 2 (v) log( 3 x 2 1) 2 < (i) log1/5 1 2 (ii) log2(4x – 2.2x + 17) > 5. (iv) log0.5 (x + 5)2 > log1/2 (3x – 1)2. (vi) logx² (2 + x) < 1 BASIC MATHS & LOGARITHM 15. Solve the following inequalities : (i) 16. 2x  1 <1 x2 (ii) x – (iv) x 2  6x  8  (vi) 2 log1/2 x  4log 2 x < 1| x | < 0 (iii) x 2  x  6 < 2x – 3 x (v) x 2  7x  10 + 9 log4    2x + 14x  20  2x 2 – 13 8 x 1 2 (4 – log16x4). Solve the following equations (i) x + 2 = 3 (ii) (iii) x x = 4 (iv) (v) (vii) x 2 x + 4 = 2 x2  3x + 1 x  2 x + 5 = 0 x 1  2 (vi) =1 |x – 3| + 2|x + 1| = 4 x – 1 – 2 = x – 3 x  2  log3 x  2 = 2 17. Find the values of x which satisfying the equation log 18. Solve for x : log 3 / 4 log 8 (x2  7 )  log1 / 2 log1 / 4 (x2  7 )1  2 . 19. Prove that product of four consecutive positive integers increased by 1 is a perfect square. 20. Find value(s) of ‘x’ satisfying equation | 2x – 1 | = 3 [x] + 2{x}. (where [ . ] and { . } denote greatest integer and 3 fractional part function respectively). 21. If (2 + i)(2 + 2i) (2 + 3i) ...... (2 + ni) = x + iy, then find the value of 5.8.13. .......(4 + n2) 22. Solve the equation |x + 1| – |x + 3| + |x – 1| – 2 |x – 2| = x + 2. 23. Find all possible solutions of equation ||x2 – 6x + 5| – |2x2 – 3x + 1|| = 3|x2 – 3x + 2| 24. Solve the following inequalities : 25. (i) |x – 3|  2 (ii) | |x – 2| – 3| 0 (iii) ||3x – 9| + 2 | > 2 (iv) |2x – 3| – |x|  3 Find the number of solutions of equation 3|x|– |2 – |x|| = 1.

Basic Maths & Logarithm Exercise # 4

Related Documents

Recommended Documents

Description

Related Documents

Almost There!

Free up your schedule!

Take 5 seconds to unlock