SOLUTION: How do you get from {{{log(a, ( (x-y)/(sqrt(x^2-y^2)) ))}}} to {{{1/2}}}{{{(log(a, (x-y))-log(a,(x+y))^"") }}}?

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Question 301241: How do you get from to ?
Answer by Edwin McCravy(20066)   (Show Source): You can put this solution on YOUR website!


Use this rule of logs:  



Now use this rule of changing radicals to fraction exponents:   and in particular  



Now use this rule of logs:  



Let's put a  written as  in front of the first term, so
we can factor out a 



Factor out 



Now let's factor  as the difference of two squares, and get .  So replacing that



Use this rule of logs:  



Remove the inner parentheses which are preceded by a negative sign:



The first two log terms inside the big parentheses are like terms so
we can combine them:



Edwin

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