Question 72626
Solve for x:
{{{ln(x+5) - ln(3) = ln(x-3)}}}
Rewrite the left side using the quotient rule of logarithms:{{{ln(M)-ln(N) = ln(M/N)}}}
{{{ln((x+5)/3) = ln(x-3)}}} Now apply the identity rule: If {{{ln(M) = ln(N)}}} then {{{M = N}}}
{{{(x+5)/3 = x-3}}} Simplify and solve for x. Multiply both sides by 3.
{{{x+5 = 3(x-3)}}}
{{{x+5 = 3x-9}}} Subtract x from both sides.
{{{5 = 2x-9}}} Add 9 to both sides.
{{{14 = 2x}}} Divide both sides by 2.
{{{7 = x}}} or {{{x = 7}}}