*Logarithm:**If a is a positive real number, other than 1 and a*^{m}= x, then we write:

*m = log*_{a}x and we say that the value of log x to the base a is m.*Examples:**(i). 10*^{3}1000 log_{10}1000 = 3.*(ii). 3*^{4}= 81 log_{3}81 = 4.*(iii). 2*^{-3}=*1**log*_{2}*1**= -3.**8**8**(iv). (.1)*^{2}= .01 log_{(.1)}.01 = 2.*Properties of Logarithms:**1. log*_{a}(xy) = log_{a}x + log_{a}y

*2. log*_{a}*x**= log*_{a}x – log_{a}y*y**3. log*_{x}x = 1*4. log*_{a}1 = 0*5. log*_{a}(x^{n}) = n(log_{a}x)*6. log*_{a}x =*1**log*_{x}a*7. log*_{a}x =*log*_{b}x*=**log x**.**log*_{b}a*log a**Common Logarithms:**Logarithms to the base 10 are known as common logarithms.**The logarithm of a number contains two parts, namely ‘characteristic’ and ‘mantissa’.**Characteristic: The internal part of the logarithm of a number is called its characteristic.**Case I: When the number is greater than 1.**In this case, the characteristic is one less than the number of digits in the left of the decimal point in the given number.**Case II: When the number is less than 1.**In this case, the characteristic is one more than the number of zeros between the decimal point and the first significant digit of the number and it is negative.**Instead of -1, -2 etc. we write 1 (one bar), 2 (two bar), etc.**Examples:-**Number**Characteristic**Number**Characteristic**654.24**2**0.6453**1**26.649**1**0.06134**2**8.3547**0**0.00123**3**Mantissa:**The decimal part of the logarithm of a number is known is its mantissa. For mantissa, we look through log table*2. If log 2 = 0.3010 and log 3 = 0.4771, the value of log _{5}512 is:A. 2.870 B. 2.967 C. 3.876 D. 3.912 Answer: Option C

Explanation:

log _{5}512= log 512 log 5 = log 2 ^{9}log (10/2) = 9 log 2 log 10 – log 2 = (9 x 0.3010) 1 – 0.3010 = 2.709 0.699 = 2709 699 = 3.876 #### If log 27 = 1.431, then the value of log 9 is:

Correct! Wrong!#### If loga/b +logb/a = log (a + b), then:

Correct! Wrong!#### If log10 2 = 0.3010, then log2 10 is equal to

Correct! Wrong!#### If log10 2 = 0.3010, the value of log10 80 is:

Correct! Wrong!#### If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to

Correct! Wrong!logarithms quizGREAT JOBShare your Results: