# SOLUTION: i need help to simplify fully this logarithm expression, please... {{{ln(A+B)-ln(A^-1+B^-1)}}} thank you!!!

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: i need help to simplify fully this logarithm expression, please... {{{ln(A+B)-ln(A^-1+B^-1)}}} thank you!!!      Log On

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 Algebra: Logarithm Solvers Lessons Answers archive Quiz In Depth

 Question 208979This question is from textbook functions modelling change : i need help to simplify fully this logarithm expression, please... thank you!!!This question is from textbook functions modelling change Answer by Theo(3458)   (Show Source): You can put this solution on YOUR website! ----- by the laws of logarithms, ----- if you let and you let , then your equation becomes: ----- your denominator of is the same as which simplifies to once you multiply the first term by and the second term by . ----- your equation becomes: this is the same as: this simplifies to: this can then be further simplified to: ----- to prove correct, substitute for A + B in the original equation and then see if you can solve the original equation and the simplified equation and get the same answer. ----- let A = 8 and let B = 15 original equation is: this becomes: = 4.787491743 ----- simplified equation is: this becomes: = 4.787491743 ----- these are both equivalent since they are equal to the same number. -----