Question 22747
Your first step is flawless!
{{{log(2,(x-2))+log(2,4)= 3}}} Now apply the Product Rule for logarithms: {{{log(b,M)+log(b,N) = log(b,(MN))}}}
{{{log(2,(x-2))+log(2,4) = log(2,(4(x-2)))}}} = 3 Simplify.
{{{log(2,(4x-8)) = 3}}} Rewrite this in exponential form: {{{log(b,x) = y}}} means {{{b^y = x}}}
{{{2^3 = 4x-8}}} Simplify and solve for x.
{{{8 = 4x-8}}} Add 8 to both sides.
{{{16 = 4x}}} Divide both sides by 4.
{{{x = 4}}}

Check: You could use your calculator but most likely it doesn't have logs to base 2.  So, you can change the base of logs from 2 to base 10, which your calculator most-likely can handle.

Change of base from 2 to 10: {{{log(2,M) = (log(10,M))/log(10,2)}}} Apply this to your problem:

{{{log(2,(4x-8)) = (log(10,(4x-8)))/log(10,2)}}} Substitute x = 4.
{{{(log(10,8))/log(10,2) = 3}}} Use your calculator.