SOLUTION: Rewrite {{{ (1/2) ln (x-3) + ln (x+2) - 6 * ln (x) }}} as a single logarithmic expression.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Rewrite {{{ (1/2) ln (x-3) + ln (x+2) - 6 * ln (x) }}} as a single logarithmic expression.      Log On


   

Question 1089990: Rewrite +%281%2F2%29+ln+%28x-3%29+%2B+ln+%28x%2B2%29+-+6+%2A+ln+%28x%29+ as a single logarithmic expression.
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
The first step here would be to remember that a constant multiplied by a logarithm can be moved to the exponent of the argument of the logarithm. So
%281%2F2%29ln%28x-3%29+=+ln%28x-3%29%5E%281%2F2%29
and
6lnx+=+ln%28x%5E6%29
Next, we remember that two logarithms added to each other can be combined into one using multiplication.
ln%28%28x-3%29%5E%281%2F2%29%29%28x%2B2%29
Lastly, two logarithms subtracted from each other can be combined into one using division.
ln%28%28%28x-3%29%5E%281%2F2%29%29%28x%2B2%29%2F%28x%5E6%29%29