Question 251005
<pre><font size = 4 color = "indigo"><b>
{{{log((n+2)) + log((8)) = log((n^2 + 7n + 10))}}}

Factor the right side:

{{{log((n+2)) + log((8)) = log(((n+2)(n+5)))}}}


Use this principle to rewrite the right side: {{{log((AB))=log((A))+log((B))}}}

{{{log((n+2)) + log((8)) = log((n+2))+log((n+5)))}}}

Subtract {{{log((n+2))}}} from both sides.

{{{ log((8))  = log((n+5))}}}

Use the principle:  {{{log((A))=log((B))}}} is equivalent to {{{A=B}}}
to remove the single logs in front of both sides of the equation:

{{{8 = n+5}}}

{{{n = 3}}}

However we must check it in the ORIGINAL equation to
make sure it is a solution:

{{{log((3+2)) + log((8)) = log((3^2 + 7(3) + 10))}}}
{{{log((5)) + log((8)) = log(((9 + 21 + 10)))}}} 
{{{log((5)) + log((8)) = log((40))}}}
Use this principle to rewrite the left side:{{{log((AB))=log((A))+log((B))}}}

{{{log((5*8))=log((40))}}}

{{{log((40))=log((40))}}}

It checks.

Edwin</pre>