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

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(13342) (Show Source): You can put this solution on YOUR website!

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by the laws of logarithms,

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if you let and you let , then your equation becomes:

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your denominator of is the same as which simplifies to once you multiply the first term by and the second term by .
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your equation becomes:

this is the same as:

this simplifies to:

this can then be further simplified to:

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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.
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let A = 8 and let B = 15
original equation is:

this becomes:
= 4.787491743
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simplified equation is:

this becomes:
= 4.787491743
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these are both equivalent since they are equal to the same number.
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