# SOLUTION: Compress the expression {{{2(ln(x-3)+ln(x))-ln(x^(2)-9)}}} into one simplified logarithm.

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Compress the expression {{{2(ln(x-3)+ln(x))-ln(x^(2)-9)}}} into one simplified logarithm.      Log On

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 Algebra: Logarithm Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on logarithm Question 258258: Compress the expression into one simplified logarithm.Answer by jsmallt9(3296)   (Show Source): You can put this solution on YOUR website! To combine logarithms we use two of the properties of logarithms: These properties require that the coefficients of the logarithms are 1's. For logarithms which have other coefficients, we have a third property which allows us to move a coefficient of a logarithm into the argument as an exponent: Inside the parentheses we find . Since this is an addition, we can use the first property to combine these: Next, we can use the third property to move the 2 from in front into the argument of the logarithm: And finally, since this is a subtraction, we can use the second property to combine the remaining logarithms: We have now condensed the expression into a single logarithm. This may be an acceptable answer. But we can simplify the argument of the logarithm. The fraction will reduce. After we factor the denominator we get: We can see that the x-3 in the denominator will cancel with one of the two (x-3)'s (it is squared, after all) leaving: Last of all we can multiply out the numerator: