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Properties of Logarithms
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sir whats the diffrence between govt expenditure and wages/income
Shahin Nisha
3 years ago
govt expenditure means money which is spent on various schemes like Food security, MNREGA etc and also in sectors like defense by the govt which are unproductive doesnt yield to govt. where as wages/income refers to individual earning i.e people earning
1. Abhishek Khurana 6 times 99 percentiler in CAT MBA from NMIMS 2009-2011 8 years of teaching experience

2. LOGARITHMS

3. Properties of Logarithm EXAMPLE 2 Find the value of x satisfying logo (24 x-41) = x (1-log,05) Solution: logo (2x + x-41)=x(1-log105) log10(2x+x-41) = x log102. logo (29 2x + X-41 = 2x x = 41

4. Properties of Logarithm EXAMPLE 3 For 0 < at 1, find the number of ordered pair (x, y) satisfying the equation logflxty|- and log ay-log al x|-log a24, Solution: we have log a2 Ixtyl = => |x+yl=a => x+y= a Also, loga (y/lx/)=loga24 => y=21x/ (2) If x > 0, then x a/3 , y = 2a/3 if x < 0, then y = 2a, x=-a possible ordered pairs (a/3,2a/3) and -a, 2a) (1)

5. Properties of Logarithm EXAMPLE 4 For N > 1, the product 1/log2N 1/logN8 .1/log32N 1/logN 128 simplifies to (A) 3/7 (B) 3/7 In2 (C)3/5In2 (D) 5/21 Solution: N/7 In 2-5/21

6. Properties of Logarithm EXAMPLE 5. If p is the smallest value of x satisfying the equation 2+28 then the value of 4P is equal to Solution: 22x-8.2x +15-0 (2x-3) (2x-5)=0 Hence smallest x is obtained by equating 2x 3 x log2 3

7. Properties of Logarithm EXAMPLE 6 If p is the smallest value of x satisfying the equation 2*+15/2 8 then the value of 4P is equal to Solution: 22t-8.2x + 15-0 (2x-3) (2x-5) = 0 2x = 3 or 2x = 5 Hence smallest x is obtained by equating 2x 3 x log2 3 p log23 4P 2 20929

8. Properties of Logarithm EXAMPLE 6 The sum of two numbers a and b is 18 and their difference is 14. The value of logo a is equal to Solution: a+b 18 a-b=14 squaring & subtract, we get 4ab 4 Hence number are reciprocal of each other logo a =-1

9. Properties of Logarithm EXAMPLE 7 #x:v10+82 /2 and y-v10-V2/2 , then the value of log2 (x2 + xy + y*), is equal to Solution: log2 ( (x+y) 2- ) But x ty 10: x-y 2:xy log2 (10-2) log2 8 3 10-2/4 2

10. Change Of base in Logarithm logo(x) loga(b)/logax) examples. Convert logs(6) to an expression with logs having a base of 5. logs(6)Flogs(3)/logs(6)