write as a single logarithm with a coefficient of 1

Question

Write log_2?(x-1)+log_2?(x+1)-log_2?(x^2-1) as a single logarithm with a coefficient of 1

Answer 1

Assume that 2 is the base of the Log:

 

   log_{2( X -1) +} log _{2 ( X +1) -} log _{2 (} X² -1) =

 

 

    log₂ ( X-1)( X+1) =  log ₂ (1) = 0

             X² - 1

 

    Using the relation ship of    Log ( AB ) = logA + log B

                                            Log ( A/ B)= LogA - Log B