Question 1008009
<pre>
{{{log((2x-3))-(log((x))^""-log((8)))}}}{{{""=""}}}{{{1}}}

Remove the large parentheses

{{{log((2x-3))-log((x))+log((8))}}}{{{""=""}}}{{{1}}}

On the first two terms, use the principle 

                {{{log((a))-log((b))=log((a/b))}}}

{{{log(((2x-3)/x))+log((8))}}}{{{""=""}}}{{{1}}}

On the two terms on the left, use the principle 

                {{{log((a))+log((b))=log((a*b))}}}

{{{log((   (  (2x-3)/x  )^""*(8)^""     ))}}}{{{""=""}}}{{{1}}}

Write 8 as {{{8/1}}}

{{{log((   (  (2x-3)/x  )^""*(8/1)^""     ))}}}{{{""=""}}}{{{1}}}

Multiply numerators and denominators:

{{{log((  (16x-24)/x        ))}}}{{{""=""}}}{{{1}}}

When the base of a log isn't written it is understood
to be 10

{{{log(10,(  (16x-24)/x        ))}}}{{{""=""}}}{{{1}}}

Use the principle that the log equation
           {{{log(b,(a))=c}}} can be written as the exponential
           equation {{{a=b^c}}}

{{{(16x-24)/x}}}{{{""=""}}}{{{10^1}}}

{{{(16x-24)/x}}}{{{""=""}}}{{{10}}}

Multiply both sides by x

{{{16x-24}}}{{{""=""}}}{{{10x}}}

{{{6x-24}}}{{{""=""}}}{{{0}}}

{{{6x}}}{{{""=""}}}{{{24}}}

{{{x}}}{{{""=""}}}{{{4}}}

Edwin</pre>