Question 84160
<pre><font size = 4><b>
what does it mean to express in terms of sums 
and defferences of logartithms? 

{{{log((sqrt(( x^2y)/z ))) }}}

Change the square root to the {{{1/2}}} power

{{{log( ((x^2y)/z)^(1/2) ) }}}

Now you can move the {{{1/2}}} power out in front
of the log, like this

{{{(1/2)log( ((x^2y)/z) ) }}}

Now the log of a QUOTIENT equals the log of the 
numerator MINUS the log of the denominator

{{{(1/2)(log((x^2y)) - log((z)))}}}

Now the log of a PRODUCT equals the log of the 
first factor {{{x^2}}} PLUS the log of the second factor {{{y}}}.

{{{(1/2)(log((x^2)) + log((y)) - log((z)))}}}

Now you can move the 2 power out in front
of the log, like this

{{{(1/2)(2*log((x)) + log((y)) - log((z)))}}}

Now you can distribute the {{{1/2}}}

{{{log((x)) + (1/2)log((y)) - (1/2)log((z))}}}

Edwin</pre>