Question 909046
<pre>
1.  {{{log(b,(x^2y^3/z))}}}

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


    {{{log(b,(x^2y^3))-log(b,(z))}}}

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

    {{{log(b,(x^2))+log(b,(y^3))-log(b,(z))}}}

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

    {{{2log(b,(x))+3log(b,(y))-log(b,(z))}}}

That's the final answer.

2.  {{{ln(x^2) - 2*ln(sqrt(x))}}}

Move the 2 coefficient on the second term as an exponent

    {{{ln(x^2) - ln((sqrt(x))^2)}}}

    {{{ln(x^2) - ln(x)}}}

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

    {{{ln(x^2/x)}}}

Simplify:

    {{{ln(x)}}}

Edwin</pre>