SOLUTION: Please help me simplify the following: {{{2LN(x-3)+LN(x+2)-6LN(x)}}} and {{{drawing(200,50,-.01,3,-.2,.1, locate(0,0, x(1-2x)^(-3/2)+(1-2x)^(-1/2)) )}}} p.s. the -3/2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me simplify the following: {{{2LN(x-3)+LN(x+2)-6LN(x)}}} and {{{drawing(200,50,-.01,3,-.2,.1, locate(0,0, x(1-2x)^(-3/2)+(1-2x)^(-1/2)) )}}} p.s. the -3/2      Log On


   

Question 205138: Please help me simplify the following:
2LN%28x-3%29%2BLN%28x%2B2%29-6LN%28x%29
and

p.s. the -3/2 and -1/2 in the equation above are exponents. meaning: x(1-2x) raised to the negative 3/2
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me simplify the following:
2LN%28x-3%29%2BLN%28x%2B2%29-6LN%28x%29

Use the principle A%2ALN%28B%29=LN%28B%5EA%29 to rewrite
the first and last terms:

LN%28x-3%29%5E2%2BLN%28x%2B2%29-LN%28x%5E6%29

Use the principle: LN%28A%29%2BLN%28B%29=LN%28A%2AB%29 to rewrite
the first two terms:

LN%28%28x-3%29%5E2%28x%2B2%29%29-LN%28x%5E6%29

Use the principle: LN%28A%29-LN%28B%29=LN%28A%2FB%29 to rewrite
the expression:

LN%28%28%28x-3%29%5E2%28x%2B2%29%29%2F%28x%5E6%29%29

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The smaller of those two exponents is -3%2F2,
so we factor out %281-2x%29%5E%28-3%2F2%29



You may wonder where I got that 1 exponent.
When you factor one power of %281-2x%29 out of
another power of %281-2x%29, you divide by 
subtracting exponents, and %28-1%2F2%29-%28-3%2F2%29=-1%2F2%2B3%2F2=2%2F2=1

So we can now erase that 1 exponent:



Removing the parentheses within parentheses:





Edwin