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Practice Questions : Part 2
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1. Abhishek Khurana 6 times 99 percentiler in CAT MBA from NMIMS 2009-2011 8 years of teaching experience

2. LOGARITHMS

3. Graphs of log function Logox is defined for x>0,a>o,a#1 71 when a> wnen Ocaci

4. Graphs of log function for O<aci logox >1 if x<a if a>1 logox >1 if xxaoo

5. Miscellaneous Examples Example 11. If log zio(x2-6x + 45) = 2, then which of the following is the value of x b. 4 c 2 d Both (1) and (2)

6. Miscellaneous Examples Example 11. If log aho(x2- 6x + 45) 2, then which of the following is the value of x b. 4 c 2 d Both (1) and (2) Solution: log 2 hole-6x + 45) = 2 log zhofx2 - 6x + 45) 2 log zho 2V10 (x2-6x+45)=40 (k2-6x+ 5)o log zho (2110)2 1or 5

7. Miscellaneous Examples Example 12. If loga(log(log2(x2+4x+4))) 1, then find the positive value of X. Solution: log:009.(log2(x2 + 4x + 4))) = 1 (log4(log2(x2 + 4x + 4))-2 (log2(x2 + 4x + 4))=16 (x2+4x + 4)=216 (x+22 =216 x+2=28 x=28-2

8. Miscellaneous Examples Example 13. Find the value of logb(2xtyoyxlob Solution: logb (2xty)lxlog, b logb (2xty) l ogx x logyx logb loga logx logy Log (2x+y) log a b: logb/loga * log(2x+y)/log blog a (2x+y)

9. Miscellaneous Examples Example 14. If logx(1/2+1/5+1/9+1/14+infinitely many terms) 2 and x > 0, then find the value of x. Solution: logx(1/2+1/5+1/9+1/14 +...infinitely many terms)2 /9+1/14 t..infinitely many terms) -P 1/1x2+1/1x5+1/3x3+1/2x7+..infinitely many terms-P... () Dividing both sides by 2, we get 1/1 x4 +1/2x5 +1/3 x6+1/4x7 +.... infinitely many terms) P/2 1/31(1-1/4)+(1/2-1/5)+(1/3-1/6)+(1/4-1171-..nfinitely many terms] P/2

10. Miscellaneous Examples 3P/2 1+1/2+1/3 p11/9 From the given equation (11/9)2 x2 x-11/9