Question 212957
Solve for x:
{{{log((2x)) = log((3))+log((x-4))}}} Apply the "product rule" to the right side.
{{{log((2x)) = log((3*(x-4)))}}} Simplify the argument of the right side.
{{{log((2x)) = log((3x-12))}}} Apply the rule: If{{{log((M)) = log((N))}}} then M=N
{{{2x = 3x-12}}} Add 12 to both sides.
{{{2x+12 = 3x}}} Subtract 2x from both sides.
{{{12 = x}}} or {{{highlight(x = 12)}}}
Check:
{{{log((2x)) = log((3))+log((x-4))}}} subsitute x = 12.
{{{log((24)) = log((3))+log((12-4))}}} Evaluate.
{{{log((24)) = log((3))+log((8))}}}
{{{1.3802 = 0.4771+0.9031}}}
{{{1.3802 = 1.3802}}}