SOLUTION: 1-Express in terms of sums and differences of logarithms: log⁡ x^2y^2/z 2-Express as a single logarithm and, if possible, simplify: lnx^2 – 2 ln

Algebra ->  Linear-equations -> SOLUTION: 1-Express in terms of sums and differences of logarithms: log⁡ x^2y^2/z 2-Express as a single logarithm and, if possible, simplify: lnx^2 – 2 ln      Log On


   

Question 909046: 1-Express in terms of sums and differences of logarithms:
log⁡ x^2y^2/z

2-Express as a single logarithm and, if possible, simplify: lnx^2 – 2 ln √x
Thank you guys in advance

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1.  log%28b%2C%28x%5E2y%5E3%2Fz%29%29

When distributing a log over a division, the division becomes subtraction:


    log%28b%2C%28x%5E2y%5E3%29%29-log%28b%2C%28z%29%29

When distributing a log over a multiplication, the multiplication becomes addition:

    log%28b%2C%28x%5E2%29%29%2Blog%28b%2C%28y%5E3%29%29-log%28b%2C%28z%29%29

In logs of exponentials, the exponents can be moved in front of the
logs as coefficients:

    2log%28b%2C%28x%29%29%2B3log%28b%2C%28y%29%29-log%28b%2C%28z%29%29

That's the final answer.

2.  ln%28x%5E2%29+-+2%2Aln%28sqrt%28x%29%29

Move the 2 coefficient on the second term as an exponent

    ln%28x%5E2%29+-+ln%28%28sqrt%28x%29%29%5E2%29

    ln%28x%5E2%29+-+ln%28x%29

When you take out a log from a subtraction, the subtraction
becomes a division:

    ln%28x%5E2%2Fx%29

Simplify:

    ln%28x%29

Edwin