Abhishek Khurana 6 times 99 percentiler in CAT MBA from NMIMS 2009-2011 8 years of teaching experience
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
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
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)
Number of digits type problem Log1oN has two parts ijintegral part (characteristics) i)Proper fraction(Mantisa) 1.No of digits in is take the log of aAb and add the characteristic part with 1. 2.No of zeros after the decimal point of a fraction. Just take log with base as 10. The number of zeros after the decimal will be equal to the integer value of the log. If there is no decimal places after the log value, then the answer is the integer value of log minus 1
Number of digits type problem Eg. for 0.01 the log will be -2.00, the number of zeros will be 1 For 0.03 the log will be -1xx the number of zeros is 1
Number of digits type problem Example 8. What is the number of digits in 2420092 Solution: 2-0.3010) Log (2^2009,-2009 Log (2) = 2009"0.3010-604.709(log Here characteristic 604 man tisa=.709 > 2A2009 has 604 + 1605 digits
Number of digits type problem Example 10. find the number of zeroes immediately after the decimal in 3A- 100? Solution: Log (3A-100)100* Log(3)--100 *0.4771-47.71 (log 2-0.4771) Here characteristic -47 manisa= .71 > 3A.100 has 47 zeroes after the decimal.
I am Abhishek Khurana. I completed my B.Com(H) from Panjab University in 2008 & my MBA from NMIMS in 2011.