Paper 4: Fundamentals of Business Mathematics & Statistic

2.26 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

(ii) 2 log (a + b) = log 9 + log a + log b.

(iii)

log (a b)^11

3 2

(^) + (^) =
{log a + lob b}

3. (i) If x^2 + y^2 = 6xy, prove that
   2 log (x + y) = log x + log y + 3 log 2

(ii) If a^2 + b^2 = 23 ab, show that log (a b)^15 + =^12 {log a + lob b}

4. If a = b^2 = c^3 = d^4 , prove that loga (abcd) =^1 +1 1 12 3 4+ +.


5. Prove : (i) log 2 log 2 log 2 16 = 1, (ii) log 2 log 2 log 3 81 = 2


6. Prove that :
   (i) logb a x logc b x loga c = 1
   (ii) logb a x logc b x loga c = logaa.
   (iii) (1+logn m x logmn x = logn x


7. (a) Show that :– (i) 16log 12log^1615 +^2524 +7log 8081 =log5

(ii) log 2log 5log^7516 −^59 + 24332 =log2

(b) Prove that

xlog -logy zylog -log log - logz xz x y = 1

8. Prove that (i) log 27 log8 log 1000 3+log120+ = 2

(ii) log 27 log8 log 1000 3+log14400+ = 4

9. Find log 7 7 7.... 7 ∞ [Ans. 1]


10. If
    logx logy logz
    y z z x x y− = − = − , show that xzy = 1


11. If loga bc = x, logb ca = y, logc, ab = z, prove that

1 1 1 1

x 1 y 1 z 1+ + + + + =

12. If l+m- 2n m+n- 2l n+l- 2mlogx = logy = logz , show that xyz = 1.