Question 70983
Solve for x:
{{{Log(x+5) - Log(x-1) = Log(x+2) - Log(x-3)}}} Apply the quotient rule for logarithms to both sides.{{{Log(M)-Log(N) = Log(M/N)}}}
{{{Log((x+5)/(x-1)) = Log((x+2)/(x-3))}}} Applying the property: If M=N then {{{Log(M) = Log(N)}}}, so:
{{{(x+5)/(x-1) = (x+2)/(x-3)}}} Simplify.
{{{(x-3)(x+5) = (x-1)(x+2)}}} Perform the indicated multiplication.
{{{x^2+2x-15 = x^2+x-2}}} Simplify.
{{{2x-15 = x-2}}} Subtract x from both sides.
{{{x-15 = -2}}} Add 15 to both sides.
{{{x = 13}}}
Check: Substitute x=13
{{{Log(13+5) - Log(13-1) = Log(13+2) - Log(13-3)}}}
{{{Log(18) - Log(12) = Log(15) - Log(10)}}}
{{{Log(18/12) = Log(15/10)}}}
{{{Log(3/2) = Log(3/2)}}}