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Practice Questions : Part 3
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sir mai janna chahta hu ki jo exam hoga isme bahut sare fonts ka character code bhi hota h or bahut ko hum key combination se bhi likh sakte h...to hume kaun sa use karna hoga exam me code ya keyboard ko jaise pra likhne ka code hota h....alt+0231 or hum isko key se bhi likh sakte h...sir please help kijiye confusion ho raha h
1. Abhishek Khurana 6 times 99 percentiler in CAT MBA from NMIMS 2009-2011 8 years of teaching experience

2. LOGARITHMS

3. Miscellaneous Examples Example 15: Find the value of the following function: log 3 x log 4 x log 5 x..x log1\$20. a)1 + log 2 b)2+ (log 2)1 c)2+ log2 d)1 (log 2)] Solution: log 3 x logs4 x log 5 xx log1,20-log2/log3 19/log 20-log 20/log 2=1+(log 2)-1 log3/log4 log5/log4t....log 194

4. Miscellaneous Examples Example 17: Find the sum of n terms of the following series: log(a/b) + log(aA2/b)+ log(aA3/b)+.... Solution: n terms of the series log(a/b) + log (a^2/b) + log(a^3/b)+ (log a - log b) +(log a2-log b)+.... (log aAn-log b) log a+ log aA2+log an3t....log aAn) - (logb + log b+... + logb) n times (1+2+ n) log a-nlogb n(n +1)/2loga-nlogb nllog a n+1/2 -loa b

5. Miscellaneous Examples Example 18:H logS4 72-b, then the value of log96 128 in terms of b is Solution: logs 72-b log2 72/ log254-b log29 +log:8/ loga9 +log26-b 2log23+3/3log23 +1 b let log23-a 2a+3/3a+1-b a b-3/2-3b logps128-7log2 2/log23 + 5l0g22 -7/a+5-2-3b/1-2b-3b-2/2b-1

6. Miscellaneous Examples Example 19: If log2(logs(x2 + 7x + 19)) , find positive value of x. Solution: logab- 1 b-a So, log2 (log3p2+7x+ 19))1 logs(x2 + 7x + 19) = 2 x2+7x +19-9 x--5,-2 Both negative, therefore, no positive value of x is possible

7. Miscellaneous Examples Example 20: If log(2-1)(x-1)I = 1, then how many values can x take? Solution: lloga-)x-1)1 1 where x-1 >0 and 2x-1#1 (as logab is defined only when b>0 and a #1) Also log a bay=> a-b Now log(2-1)(x-1) =1 or log a-)/x-1)-1 case 1 : log(2-1) (x-1) = 1 2x-13x-1 =>x=0 not possible as x>1

8. Miscellaneous Examples Example 21: Minimum value for the expression: 4logiox-logx (1/1000) where x>1 is a. 8 C. 4V3 d. 7 Solution: 4loghox-log (1/1000) 4log1o x 3/logiox using concept of AM > GM, 410g10 x + 3/log,ox/2 >s( 4logo x" 3/logeX

9. Miscellaneous Examples Example 22: log(mtn3),log(m3 n3 )log(m2n2 )are the first three terms of an Arithmetic Progression. If the 8th term of the Arithmetic Progression is log(m n ), what is the value of a? Solution: log A, log B and log C are in AP, then A, B, and C are in G.P where BA2 AC. n=m The 8th term if the series would be n . So, the value of a = 0.